Falko Baustian

University of Rostock · Institut für Mathematik

We investigate the basis properties of sequences of Fučík eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in L2(0,π) and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fučík eigenvalues which guarantee that the corresponding Fučík eigenfun...

We establish sufficient assumptions on sequences of Fučík eigenvalues of the one-dimensional Laplacian which guarantee that the corresponding Fučík eigenfunctions form a Riesz basis in L2(0,π).

The aim of the present study was to identify the parasite fauna of cultured rainbow trout (Oncorhynchus mykiss Walbaum, 1792) and Arctic charr (Salvelinus alpinus (L.)) from a flow-through aquaculture system at Lake Tollense in northern Germany. The fish were sampled during different seasons in 2018 from an open freshwater raceway. For rainbow trou...

In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE approach allows their easy incorporation. The aim of this paper is to show how to solve the PDE analytically in the...

Analytic smooth solutions of a general, strongly parabolic semi-linear Cauchy problem of $2m$-th order in $\mathbb{R}^N\times (0,T)$ with analytic coefficients (in space and time variables) and analytic initial data (in space variables) are investigated. They are expressed in terms of holomorphic continuation of global (weak) solutions to the syste...

We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,\pi)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fucik eigenvalues which guarantee that the corresponding Fucik eig...

We provide improved sufficient assumptions on sequences of Fucik eigenvalues of the one-dimensional Dirichlet Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\pi)$. For that purpose, we introduce a criterion for a sequence in a Hilbert space to be a Riesz basis.

We establish sufficient assumptions on sequences of Fucik eigenvalues of the one-dimensional Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\pi)$.

Let [Formula: see text] be an arithmetic function with [Formula: see text] and let [Formula: see text] be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behavior of [Formula: see text] with regard to the asymptotic behavior of [Formula: see text] assuming that the latter one grows or decays with at most polynomial...

In this paper we study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial diferential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare obtaine...

Let $f(n)$ be an arithmetic function with $f(1)\neq0$ and let $f^{-1}(n)$ be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behaviour of $|f^{-1}(n)|$ with regard to the asymptotic behaviour of $|f(n)|$ assuming that the latter one grows or decays with at most polynomial or exponential speed. As a by-product, we o...

In this paper, we introduce a unifying approach to option pricing under continuous‐time stochastic volatility models with jumps. For European style options, a new semi‐closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro‐differential equation. This approach is successfully applied to...