Journal article

Existence And Uniqueness Of A Mild Solution To The Stochastic Heat Equation With White And Fractional Noises

Year:

2018

Published in:

Theory of Probability and Mathematical Statistics

Authors:

, ,

Fractional Brownian motion

stochastic partial differential equation

Green’s function

We prove the existence and uniqueness of a mild solution for a class of nonautonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset D ⊂ Rd and involving standard and fractional L2(D)-valued Brownian motions. We assume that the coefficients are homogeneous, Lipschitz continuous, and the coefficient at the fractional Brownian motion is an affine function.

Other publications by

80 publications found

Journal article

Wreath Powers Of Monogenic Inverse Monoids

Publisher: Semigroup Forum

Authors: Georgiy Shevchenko, A. Oliynyk, Eugenia Kochubinska

Journal article

Real Harmonizable Multifractional Stable Process And Its Local Properties

Publisher: Stochastic Processes and their Applications

Authors: Georgiy Shevchenko, Marco Dozzi, Yulia Mishura, Kostiantyn Ral’chenko

Journal article

Rate Of Convergence Of Euler Approximations Of Solution To Mixed Stochastic Differential Equation Involving Brownian Motion And Fractional Brownian Motion

Publisher: Random Operators and Stochastic Equations

Authors: Georgiy Shevchenko, Yulia Mishura

Journal article

Boundary Non‑Crossing Probabilities Of Gaussian Processes: Sharp Bounds And Asymptotics

Publisher: Journal of Theoretical Probability

Authors: Georgiy Shevchenko, Enkelejd Hashorva, Yulia Mishura

Journal article

Approximation Schemes For Stochastic Differential Equations In Hilbert Space

Publisher: Theory of Probability & Its Applications

Authors: Georgiy Shevchenko, Yulia Mishura

Journal article

Stochastic Selection Problem For A Stratonovich Sde With Power Non‑Linearity

Publisher: Bernoulli

Authors: Georgiy Shevchenko, Ilya Pavlyukevich

Journal article

Integral Representation With Respect To Fractional Brownian Motion Under A Log‑Hölder Assumption

Publisher: Modern Stochastics: Theory and Applications

Authors: Georgiy Shevchenko, Taras Shalaiko

Journal article

The Rate Of Convergence For Euler Approximations Of Solutions Of Stochastic Differential Equations Driven By Fractional Brownian Motion

Publisher: Stochastics

Authors: Georgiy Shevchenko, Yulia Mishura

Existence And Uniqueness Of Mild Solution To Stochastic Heat Equation With White And Fractional Noises

Publisher: arxiv

Authors: Georgiy Shevchenko, Kostiantyn Prontenko, Yulia Mishura

Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko