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Citations since 2017
5 Research Items
September 2007 - November 2016
The application of the method of boundary integral equations is considered for studying the stress state of flat viscoelastic bodies with inclusions. The method is based on the use of complex potentials and the apparatus of generalized functions. An analytical solution of the problem is obtained for a half-plane with inclusions of arbitrary shape....
We consider a fractionally integrated Bessel process defined by Y s δ , H = ∫ 0 ∞ ( u H − ( 1 / 2 ) − ( u − s ) + H − ( 1 / 2 ) ) d X u δ , where X δ is the Bessel process of dimension δ > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder conti...
An approach for approximating unknown densities of potentials in the study of the stressed state of a flat viscoelastic piecewise homogeneous body with inclusions, bounded by piecewise smooth contours, is proposed. The method is based on the construction of a system of boundary-time integral equations to determine the unknown densities of potential...
Complex random variables and processes with a vanishing pseudo-correlation are called proper. There is a class of stationary proper complex random processes that have a stable correlation function. In the present article we consider real stationary Gaussian processes with a stable correlation function. It is shown that the trajectories of stationar...
In the present article we study properties of random processes from the Banach spaces F ψ (Ω). Estimates are obtained for distributions of semi-norms of sample functions of processes from F ψ (Ω) spaces, defined on the infinite interval [0,∞), in Hölder spaces.
The Lipschitz continuity is studied for stochastic processes X = (X(t), t ∈ T) belonging to the Banach spaces Fψ(Ω), where (T, ρ) is a metric space. Some bounds for the distributions of the norms of stochastic processes in the Lipschitz spaces are also obtained.
A theorem about modules of continuity of random processes from the Orlicz spaces of random variables is proved. Examples of its application are presented.