Journal article

Heat Equation In A Multidimensional Domain With A General Stochastic Measure

Year:

2016

Published in:

Theory of Probability and Mathematical Statistics

Authors:

Stochastic measure

stochastic heat equation

mild solution

Hölder condition

Besov space

Stochastic heat equation on [0,T]×R^d, d≥1, driven by a general stochastic measure µ(t), t∈[0,T], is studied in this paper. The existence, uniqueness, and Hölder regularity of a mild solution are proved.

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Other publications by

67 publications found

2011

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Real Harmonizable Multifractional Stable Process And Its Local Properties

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

2008

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

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2015

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Publisher: Statistical Inference for Stochastic Processes

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2011

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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

2013

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Publisher: Statistics & Probability Letters

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2021

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

Publisher: Journal of Theoretical Probability

Authors: Georgiy Shevchenko, Enkelejd Hashorva, Yulia Mishura

2014

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Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko

2007

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Approximation Schemes For Stochastic Differential Equations In Hilbert Space

Publisher: Theory of Probability & Its Applications

Authors: Georgiy Shevchenko, Yulia Mishura

2018

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

Publisher: arxiv

Authors: Georgiy Shevchenko, Kostiantyn Prontenko, Yulia Mishura

2022

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Tail Measures And Regular Variation

Publisher: Electronic Journal of Probability

Authors: Georgiy Shevchenko, Martin Bladt, Enkelejd Hashorva