A note on maximal estimates for stochastic convolutions [PDF]
arXiv, 2010 In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.
arxiv
Shell Model of Turbulence Perturbed by Lévy Noise [PDF]
arXiv, 2010 In this work we prove the existence and uniqueness of the strong solution of the shell model of turbulence perturbed by L\'{e}vy noise. The local monotonicity arguments have been exploited in the proofs.
arxiv
Stochastic Navier-Stokes Equations on a Thin Spherical Domain. [PDF]
Appl Math Optim, 2021 Brzeźniak Z, Dhariwal G, Le Gia QT.
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Construction of program control with probability one for a dynamical system with Poisson perturbations [PDF]
Bulletin of PNU. No 2 (21) 2011. (in Russian), 2011 In article we construct the program control with probability one for a dynamical system with Poisson perturbations.
arxiv
Riemann integral of a random function and the parabolic equation with a general stochastic measure [PDF]
Theory of Probability and Mathematical Statistics, v. 87 (2013),
185-198, 2012 For stochastic parabolic equation driven by a general stochastic measure, the weak solution is obtained. The integral of a random function in the equation is considered as a limit in probability of Riemann integral sums. Basic properties of such integrals are studied in the paper.
arxiv
The construction of the program control with probability one for stochastic dynamic systems with jumps [PDF]
arXiv, 2012 Investigate the stochastic dynamic non-linear system with the Wiener and the Poisson perturbations. For such systems we construct the program control with probability one, which allows this system to move on the given trajectory. In this case the control program is solution of the algebraic system of linear equations.
arxiv
Existence and uniqueness of invariant measures for SPDEs with two reflecting walls [PDF]
arXiv, 2012 In this article, we study stochastic partial differential equations with two reflecting walls, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of invariant measures is established under appropriate conditions. The strong Feller property is also obtained.
arxiv
Large Deviation Principle for Some Measure-Valued Processes [PDF]
arXiv, 2012 We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian motion and Fleming-Viot processes.
arxiv
Finite speed of propagation for stochastic porous media equations [PDF]
arXiv, 2012 We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving signal, thus including fractional Brownian motion for all Hurst parameters. The explicit estimates are
arxiv
On signed measure valued solutions of stochastic evolution equations [PDF]
arXiv, 2013 We study existence, uniqueness and mass conservation of signed measure valued solutions of a class of stochastic evolution equations with respect to the Wiener sheet, including as particular cases the stochastic versions of the regularized two-dimensional Navier-Stokes equations in vorticity form introduced by Kotelenez.
arxiv