Working paper

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

Year:

2018

Published in:

arxiv
Probability
white and fractional noises
mild solution
stochastic heat equation

We prove the existence and uniqueness of a mild solution for a class of non-autonomous 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

68 publications found

2020
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Comparative Biomechanical Characteristics of One‑Arm Hang in Climbing for Beginners and Qualified Athletes

Publisher: Acta of Bioengineering and Biomechanics

Authors: Hanna Kniaz, Sergii Kozin, Danil Safronov, Zhanneta Kozina, Olexsii Proskurnia, Kostiantyn Prontenko, Olena Lahno, Volodymyr Goncharenko, Alexandr Kholodniy

2021
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

2014
Working paper

Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko

2007
Journal article

Approximation Schemes For Stochastic Differential Equations In Hilbert Space

Publisher: Theory of Probability & Its Applications

Authors: Georgiy Shevchenko, Yulia Mishura

2013
Journal article

Malliavin Regularity Of Solutions To Mixed Stochastic Differential Equations

Publisher: Statistics & Probability Letters

Authors: Georgiy Shevchenko, Taras Shalaiko

2011
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

2008
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

2015
Journal article

Asymptotic Behavior Of Mixed Power Variations And Statistical Estimation In Mixed Models

Publisher: Statistical Inference for Stochastic Processes

Authors: Georgiy Shevchenko, Yulia Mishura, Marco Dozzi

2011
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

2022
Journal article

Tail Measures And Regular Variation

Publisher: Electronic Journal of Probability

Authors: Georgiy Shevchenko, Martin Bladt, Enkelejd Hashorva