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For a real-valued stochastic process (X t) t≥0 we establish conditions under which the inverse first-passage time problem has a solution for any random variable ξ > 0. For Markov processes we give additional conditions under which the solutions are unique and solutions corresponding to ordered initial states fulfill a comparison principle. As examp...
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Cellular scale decision-making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems which model this process are computationally challenging due to their complex geometry and mixed boundary conditions together with intrinsical...
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This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for I(1) linear processes, using canonical correlation analysis and functional approximation of Brownian Motions. It proposes inference criteria based on the estimation of the number of common trends in various subsets of variables, and compare...
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We establish new instances of the cutoff phenomenon for geodesic paths and for the Brownian motion on compact hyperbolic manifolds. We prove that for any fixed compact hyperbolic manifold, the geodesic path started on a spatially localized initial condition exhibits cutoff. Our work also extends results obtained by Golubev and Kamber on hyperbolic...
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We derive first-order Pontryagin optimality conditions for stochastic optimal control with deterministic controls for systems modeled by rough differential equations (RDE) driven by Gaussian rough paths. This Pontryagin Maximum Principle (PMP) applies to systems following stochastic differential equations (SDE) driven by Brownian motion, yet it doe...
Article
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In this work, we study the qualitative properties of a simple mathematical model that can be applied to the reversal of antimicrobial resistance. In particular, we analyze the model from three perspectives: ordinary differential equations (ODEs), stochastic differential equations (SDEs) driven by Brownian motion, and fractional differential equatio...
Article
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We propose a way to detect gravitons by replicating the Brownian motion experiment. The number $$N_g$$ N g of gravitons can be large enough for the stochastic gravitational noise produced by them to displace a massive test particle in a physical system, allowing for the detection of gravitons. Possible experiments to detect gravitons are proposed i...
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Nanoparticles show superior potential for enhancing thermal properties compared to conventional particle–liquid suspensions. This investigation delves into magnetohydrodynamics (MHD) drift, heat, and mass transfer effects within a Jeffery nanoparticle liquid. The study includes transference equations that consider the influences of thermophoresis a...
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We address the problem of estimating the drift parameter in a system of $N$ interacting particles driven by additive fractional Brownian motion of Hurst index \( H \geq 1/2 \). Considering continuous observation of the interacting particles over a fixed interval \([0, T]\), we examine the asymptotic regime as \( N \to \infty \). Our main tool is a...
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This article began when icy balls that may be a new kind of star were observed in space. They seem to have the contradictory characteristic of being cold enough to have abundant ice, but also possess infrared emission like a hot star. The contradiction could be resolved using a mathematics called vector-tensor-scalar geometry which is based on a pa...
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Effective heat and mass transfer is crucial for enhancing efficiency and performance, particularly under varying flow conditions in devices such as heat exchangers, microfluidic systems, and chemical reactors. The current study investigates the effect of novel combination of unsteady condition and multiphase flow effect on hybrid nanofluid (HNF) co...
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Magnetic skyrmions, which exhibit Brownian motion in solid-state systems, are promising candidates as signal carriers for Brownian computing. However, successfully implementing such systems requires two critical components: a Hub to connect multiple wires and a C-join to synchronize the skyrmion signal carriers. While the former has been successful...
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This article investigates solar energy storage due to the Jeffrey hybrid nanofluid flow containing gyrotactic microorganisms through a porous medium for parabolic trough solar collectors. The mechanism of thermophoresis and Brownian motion for the graphene and silver nanoparticles are also encountered in the suspension of water-based heat transfer...
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In this study, we investigate the magnetohydrodynamic irreversibility generation that arises in weakly conducting dissipative Casson fluid flow due to the moving Riga plate in an electro-magnetohydrodynamic actuator. The consequences of Joule heating, chemical reaction, heat source, wall suction, and thermal radiation are also assessed in the fluid...
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Efficient management of bankruptcy risk requires treating distant-to-default (DD) stochastically as long as historical stock prices move randomly and, thus, do not guarantee that history may repeat itself. Using long-term data that date back to 1952–2023, including the nonfinancial companies listed in the Dow Jones Industrial Average and National A...
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We elaborate on the theorem saying that as permeability coefficients of snapping‐out Brownian motions tend to infinity in such a way that their ratio remains constant, these processes converge to a skew Brownian motion. In particular, convergence of the related semigroups, cosine families, and projections is discussed.
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Quantitative traits are a source of evolutionary information often difficult to handle in cladistics. Tools exist to analyse this kind of data without subjective discretization, avoiding biases in the delimitation of categorical states. Nonetheless, our ability to accurately infer relationships from continuous characters is incompletely understood,...
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Ancestral state reconstruction is a phylogenetic comparative method that involves estimating the unknown trait values of hypothetical ancestral taxa at internal nodes of a phylogenetic tree. Ancestral state reconstruction has long been, and continues to remain, among the most popular analyses in phylogenetic comparative research. In this review, I...
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We analyze the equivalents of the celebrated arcsine laws for Brownian motion undergoing Poissonian resetting. We obtain closed-form formulae for the probability density functions of the corresponding random variables in the cases of the first and second arcsine law. Furthermore, we obtain numerical results for the third law.
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We investigate the evolution of the rightmost particle for the locally inhomogeneous branching Brownian motion. The branching rate measure is the compactly supported Kato class measure. This process is characterized by the Schrödinger-type operator. The asymptotic properties are determined by the characteristic quantities such as the eigenvalue and...
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We show that the spine of the Fleming–Viot process driven by Brownian motion and starting with two particles in a bounded interval has a different law from that of Brownian motion conditioned to stay in the interval forever. Furthermore, we estimate the “extra drift.”
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Occupation times of a stochastic process models the amount of time the process spends inside a spatial interval during a certain finite time horizon. It appears in the fiber lay-down process in nonwoven production industry. The occupation time can be interpreted as the mass of fiber material deposited inside some region. From application point of v...
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Finite dimensional (FD) models \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_d$$\end{document}, i.e., deterministic functions of time and finite sets of d random va...
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The influence of laser-induced active Brownian motion on dust-acoustic instability in the colloidal plasma of a direct current glow discharge was experimentally studied. The dust structure was formed by spherical monodisperse melamine-formaldehyde particles with a partial copper coating (Janus particles). It is shown that with increasing laser radi...
Article
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This paper considers the Darcy–Forchheimer flow over a micropolar nanofluid by using an intelligent backpropagated neural network with Levenberg–Marquardt scheme. The PDEs governing the DFF-MNFM are reduced into ODEs through some appropriate transformations. A reference dataset is prepared from HAM by changing several key parameters, such as the po...
Preprint
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We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall -- an outcome that is harmful in case of allergens and pathogens but beneficial in case of aerosolized drugs. We adopt the weighted-res...
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Wall jet flows are frequently used in cooling electronic equipment, in which a high-velocity fluid is released from a small opening along a flat plate. This kind of system improves heat transfer rates, making it useful for controlling thermal loads in tiny electrical systems. This research intends to provide a novel numerical solution to a non-Newt...
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We propose a new financial model called the generalized fractional Brownian motion Heston exponential Hull–White model, which has stochastic volatility and interest rate, long memory, and heavy tail distribution. Based on the market price of the volatility and delta hedging strategies, we propose a partial differential equation (PDE) to obtain the...
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We study the dynamical phase transitions (DPTs) appearing for a single Brownian particle without drift. We first explore how first-order DPTs in large deviations can be found even for a single Brownian particle without any force upon raising the dimension to higher than 4. The DPTs accompany temporal phase separations in their dynamical paths, whic...
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Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for the short-term limit of this second derivative in terms of the first and second Malliavin derivatives of the vol...
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We study multidimensional discontinuous backward stochastic differential equations in a filtration that supports both a Brownian motion and an independent integer-valued random measure. Under suitable $\mathbb{L}^p$-integrability conditions on the data, we establish the existence and uniqueness of $\mathbb{L}^p$-solutions for both cases: $p \geq 2$...
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Path planning is of great research significance as it is key to affecting the efficiency and safety of mobile robot autonomous navigation task execution. The traditional gray wolf optimization algorithm is widely used in the field of path planning due to its simple structure, few parameters, and easy implementation, but the algorithm still suffers...
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The study explores the properties of mass and heat transfer in a time-dependent, unsteady magnetohydrodynamic (MHD) flow over a permeable, radiative, and expanded surface, incorporating bio-convection, nanoparticle suspension, and gyrotactic bacteria dynamics. The model considers the effects of emission, speed slip, and bio-thermal convection in th...
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High-gradient magnetic chromatography (HGMC) is a technique for selectively separating magnetic particles according to their magnetic susceptibilities. We develop a mathematical model for HGMC that includes the effects of magnetic force, Brownian motion, gravity, and viscous drag. We then use this model to interpret recently reported experimental r...
Preprint
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We give a unified proof of the Yamada-Watanabe-Engelbert theorem for various notions of solutions for SPDEs in Banach spaces with cylindrical Wiener noise. We use Kurtz' generalization of the theorems of Yamada, Watanabe and Engelbert. Moreover, we deduce the classical Yamada-Watanabe theorem for SPDEs, with a slightly different notion of 'unique s...
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In this article, we introduce a new stochastic process called the sub-fractional G -Brownian motion, which serves as an intermediate between the G -Brownian motion and the fractional G -Brownian motion. Although the sub-fractional G-Brownian motion shares some properties with the fractional G-Brownian motion, it features nonstationary increments. W...
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In this study, we look at the stochastic Heisenberg Ferromagnetic equation (SHFE) perturbed in the Itô sense by multiplicative Brownian motion. The SHFE is transformed into a different Heisenberg Ferromagnetic equation with random variable coefficients (HFE-RVCs) utilizing the proper transformation. To provide novel solutions for trigonometric func...
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In this study, we consider the stochastic Quantum Zakharov-Kuznetsov equation (SQZKE) perturbed in the Itô sense by multiplicative Brownian motion. We employ a suitable transformation for changing the SQZKE to another QZKE with random variable coefficients (QZKE-RVCs). Utilizing the modified extended tanh function method and the Jacobi elliptic fun...
Preprint
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The paper is devoted to the properties of the entropy of the exponent-Wiener-integral fractional Gaussian process (EWIFG-process), that is a Wiener integral of the exponent with respect to fractional Brownian motion. Unlike fractional Brownian motion, whose entropy has very simple monotonicity properties in Hurst index, the behavior of the entropy...
Article
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This investigation was carried out to study the microrotational flow of nanoliquids across an extensible surface. The dispersion of nanomaterials in everyday liquids is becoming a major focus of nanotechnology. Dispersing nanoparticles in a conventional liquid increases its thermal conductivity, which is useful for both generating and transferring...
Article
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Nanofluid holds features to improve the thermal efficiency of various technological fluids. These materials have a broad range of industrial and engineering utilizations including energy production, cooling of engines, thermal exchanges, thermal structures, extrusion procedures hybrid power plants, etc. Application in the stated sectors proposed an...
Article
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This study evaluates the unsteady laminar flow and heat and mass transfer of a nanofluid in the appearance of gyrotactic microorganisms. In this analysis, using the Darcy–Forchheimer flow inside the vicinity of a nonlinearly stretched surface with Brownian motion and thermophoresis impacts. Similarity conversion is familiar with reduced governing m...
Preprint
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Lévy flights (LF), a concept originating in statistical physics, describe random walks in which the step lengths follow a heavy-tailed probability distribution, often a power law. Unlike Brownian motion, where step lengths are constrained within a narrow range, LF are characterized by the coexistence of many short steps interspersed with occasional...
Preprint
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We propose that the core mass function (CMF) can be driven by filament fragmentation. To model a star-forming system of filaments and fibers, we develop a fractal and turbulent tree with a fractal dimension of 2 and a Larson's law exponent ($\beta$) of 0.5. The fragmentation driven by convergent flows along the splines of the fractal tree yields a...
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Deriving an arrow of time from time-reversal symmetric microscopic dynamics is a fundamental open problem in many areas of physics, ranging from cosmology, to particle physics, to thermodynamics and statistical mechanics. Here we focus on the derivation of the arrow of time in open quantum systems and study precisely how time-reversal symmetry is b...
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The study of hematopoietic stem cell (HSCs) maintenance and differentiation to supply the hematopoietic system presents unique challenges, given the complex regulation of the process and the difficulty in observing cellular interactions in the stem cell niche. Quantitative methods and tools have emerged as valuable mechanisms to address this issue;...
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People have approached forecasting commodity prices in various ways because of their significant impact on the global economy. Investors and governmental agencies would benefit from an accurate forecasting tool for a valuable commodity. The recent use of silver in healthcare and technology has driven a significant rise in its value as a commodity....
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This paper presents an original and comprehensive comparative analysis of eight fractal analysis methods, including Box Counting, Compass, Detrended Fluctuation Analysis, Dynamical Fractal Approach, Hurst, Mass, Modified Mass, and Persistence. These methods are applied to artificially generated fractal data, such as Weierstrass–Mandelbrot functions...
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This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a càdlàg uniformly integrable martingale and, $v$ is a continuous process with integrable variations such that $v_{0}=0$ and $dv$ is carried by $H$. First, we extend this not...
Article
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In this paper, we consider a class of stochastic differential equations driven by multiplicative α-stable (0<α<2) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a conc...
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Let {Y (t), t ≥ 0} be a controlled geometric Brownian motion and X(t) be the integral of Y (t). The problem of minimizing the expected time that the ratio X(t)/Y (t) will spend between two constants is considered. The optimal control is obtained explicitly in terms of special functions. A risk-sensitive version of the cost criterion is also propose...
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The self-catalytic branching Brownian motions (SBBM) are extensions of the classical one-dimensional branching Brownian motions by incorporating pairwise branchings catalyzed by the intersection local times of the particle pairs. These processes naturally arise as the moment duals of certain reaction-diffusion equations perturbed by multiplicative...
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This study examines the transient magnetohydrodynamic (MHD) flow of Walter's‐B viscoelastic fluid over a vertical porous plate within a porous medium, considering the effects of radiation and chemical processes. The nonlinear flow control equations are solved using a closed‐loop method, producing detailed numerical solutions for velocity, temperatu...
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This paper considers the large N limit of Wilson loops for the two-dimensional Euclidean Yang–Mills measure on all orientable compact surfaces of genus larger or equal to $1$, with a structure group given by a classical compact matrix Lie group. Our main theorem shows the convergence of all Wilson loops in probability, given that it holds true on a...
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For $d > 2$ and $\gamma \in (0, \sqrt{2d})$, we study the Liouville Brownian motion associated with the whole-space log-correlated Gaussian field in $\mathbb{R}^d$. We compute its spectral dimension, i.e., the short-time asymptotics of the heat kernel along the diagonal, which, in contrast to the two-dimensional case, depends on both $\gamma$ and o...
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The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of these systems remains partial. In this work, we consider a lattice gas model of active-passive particle mixture...
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Given a compact set $E\subset\mathbb{R}^d$ we investigate for which values of $m$ we have that $\dim_\theta P_V(E)=m$ or $\dim_\theta P_V(E)=\dim_\theta E$ for $\gamma_{d,m}-$almost all $V\in G(d,m)$. Our result can be extended to more general functions that include orthogonal projections and fractional Brownian motion. As a particular case, lettin...
Article
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Stochastic problems have become an indispensable tool in modeling complex systems across various disciplines, including biology, chemistry, physics, economics, finance, mechanics and several areas. In this paper, we are concerning with the nonlocal problem of the integro-fractional orders stochastic differential equation dX(t) dt = f(t,DX(t)) + g(t...
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We investigate sorting Rayleigh optical particles up to several nanometers in size during Brownian motion in a tilted periodic potential with multiple deep wells. The wells are induced by optical bound states in the continuum within a system of parallel photonic crystal slabs immersed in a liquid. The Brownian dynamics of the particles is significa...
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Objective. Magnetic resonance imaging (MRI), functional MRI (fMRI) and other neuroimaging techniques are routinely used in medical diagnosis, cognitive neuroscience or recently in brain decoding. They produce three- or four-dimensional scans reflecting the geometry of brain tissue or activity, which is highly correlated temporally and spatially. Wh...
Conference Paper
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The attempts to construct a model that correctly replicates the market realities reached the maturity to challenge the standard Brownian Motion (sBM) as the stochasticity driver of the Black-Scholes log-returns. Recent researches provide arguments to generalize the sBM with a fractional Brownian Motion (fBM) [9, 17]. The capability of fBM-based mod...
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We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness of solutions in $\mathbb{L}^p$ for $p \in (1,2]$. Our results apply to generators that are stochastic monotone...
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In this paper, we introduce and study McKean-Vlasov processes of bridge type. Specifically, we examine a stochastic differential equation (SDE) of the form: $$\mathrm{d} \xi_t=-\mu(t,\mathbb{E}[\varphi_1(\xi_t)]) \frac{\xi_t}{T-t} \mathrm{d} t+\sigma(t,\mathbb{E}[\varphi_2(\xi_t)]) \mathrm{d} W_t,\,\, t<T,$$ where $\mu$ and $\sigma$ are determinist...
Article
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We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that includes strong existence, path-by-path uniqueness, existence of a solution flow of diffeomorphisms, Malliavin...
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With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter, we prove and make use a priori bounds, in the complex plane, for the Hermite functions; as well as a new approa...
Article
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In this paper, the quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions is studied. Using the Wightman functions, general expressions for the renormalized dispersion of the physical momentum are derived. Distinct...
Article
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Barrier crossing is a widespread phenomenon across natural and engineering systems. While abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process have yet to be linked quantitatively to easily measurable observables. We bridge this gap by developing a microscopic representation of...
Preprint
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This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then, the existence and uniqueness of weak pullback mean random attractors for the equations {are} established by defi...
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Let $W= \{W(t): t \in \mathbb{R}_+^N \}$ be an $(N, d)$-Brownian sheet and let $E \subset (0, \infty)^N$ and $F \subset \mathbb{R}^d$ be compact sets. We prove a necessary and sufficient condition for $W(E)$ to intersect $F$ with positive probability and determine the essential supremum of the Hausdorff dimension of the intersection set $W(E)\cap F...
Article
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We report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolution in those rate equations can be described by 1-...
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Suspensions of self-propelled objects represent a novel paradigm in colloidal science. In such active baths traditional concepts, such as Brownian motion, fluctuation-dissipation relations, and work extraction from heat reservoirs, must be extended beyond the conventional framework of thermal baths. Unlike thermal baths, which are characterized by...
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We record and analyze the movement patterns of the marsupial {\it Didelphis aurita} at different temporal scales. Animals trajectories are collected at a daily scale by using spool-and-line techniques, and with the help of radio-tracking devices animals traveled distances are estimated at intervals of weeks. Small-scale movements are well described...
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Intermediate-mass ratio inspirals (IMRIs) formed by stellar-mass compact objects orbiting intermediate-mass black holes will be detected by future gravitational wave (GW) observatories like TianQin, LISA, and AION. We study a set of 100 IMRI systems in globular clusters obtained from MOCCA simulations to study their detectability. Furthermore, we m...
Article
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Phase transitions are fundamental phenomena in physics that have been extensively studied owing to their applications across diverse industrial sectors, including energy, power, healthcare, and the environment. An example of such applications in the energy sector is thermal energy storage using phase change materials. In such systems, and indeed in...
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This article provides a brief overview on a range of basic dynamical systems that conform to the logarithmic distribution of significant digits known as Benford's law. As presented here, most theorems are special cases of known, more general results about dynamical systems whose orbits or trajectories follow this logarithmic law, in one way or anot...
Article
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We consider the eigenvectors of the principal minor of dimension n < N of the Dyson Brownian motion in RN and investigate their asymptotic overlaps with the eigenvectors of the full matrix in the limit of large dimension. We explicitly compute the limiting rescaled mean squared overlaps in the large n,N limit with n/N tending to a fixed ratio q, fo...
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In this work, we generalize the concept of bisimulation metric in order to metrize the behaviour of continuous-time processes. Similarly to what is done for discrete-time systems, we follow two approaches and show that they coincide: as a fixpoint of a functional and through a real-valued logic. The whole discrete-time approach relies entirely on t...
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We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional geometrically embedded data, especially for neuroimaging data which is highly correlated temporally and spatially...