Approximations for a solution to stochastic heat equation with stable noise

We consider a Cauchy problem for stochastic heat equation driven by a real harmonizable fractional stable process Z with Hurst parameter $H>1/2$ and stability index $\alpha >1$. It is shown that the approximations for its solution, which are defined by truncating the LePage series for Z, conve...

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Main Authors:	Larysa Pryhara, Georgiy Shevchenko
Format:	Article
Language:	English
Published:	VTeX 2016-06-01
Series:	Modern Stochastics: Theory and Applications
Subjects:	Heat equation real harmonizable fractional stable process LePage series stable random measure general stochastic measure
Online Access:	https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA56

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spelling	doaj-066a1f02f12f4358aa5becb6df9f510d2020-11-25T01:20:10ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542016-06-013213314410.15559/16-VMSTA56Approximations for a solution to stochastic heat equation with stable noiseLarysa Pryhara0Georgiy Shevchenko1Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska 64/11, 01601 Kyiv, UkraineMechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska 64/11, 01601 Kyiv, UkraineWe consider a Cauchy problem for stochastic heat equation driven by a real harmonizable fractional stable process Z with Hurst parameter $H>1/2$ and stability index $\alpha >1$. It is shown that the approximations for its solution, which are defined by truncating the LePage series for Z, converge to the solution.https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA56Heat equationreal harmonizable fractional stable processLePage seriesstable random measuregeneral stochastic measure
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Larysa Pryhara Georgiy Shevchenko
spellingShingle	Larysa Pryhara Georgiy Shevchenko Approximations for a solution to stochastic heat equation with stable noise Modern Stochastics: Theory and Applications Heat equation real harmonizable fractional stable process LePage series stable random measure general stochastic measure
author_facet	Larysa Pryhara Georgiy Shevchenko
author_sort	Larysa Pryhara
title	Approximations for a solution to stochastic heat equation with stable noise
title_short	Approximations for a solution to stochastic heat equation with stable noise
title_full	Approximations for a solution to stochastic heat equation with stable noise
title_fullStr	Approximations for a solution to stochastic heat equation with stable noise
title_full_unstemmed	Approximations for a solution to stochastic heat equation with stable noise
title_sort	approximations for a solution to stochastic heat equation with stable noise
publisher	VTeX
series	Modern Stochastics: Theory and Applications
issn	2351-6046 2351-6054
publishDate	2016-06-01
description	We consider a Cauchy problem for stochastic heat equation driven by a real harmonizable fractional stable process Z with Hurst parameter $H>1/2$ and stability index $\alpha >1$. It is shown that the approximations for its solution, which are defined by truncating the LePage series for Z, converge to the solution.
topic	Heat equation real harmonizable fractional stable process LePage series stable random measure general stochastic measure
url	https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA56
work_keys_str_mv	AT larysapryhara approximationsforasolutiontostochasticheatequationwithstablenoise AT georgiyshevchenko approximationsforasolutiontostochasticheatequationwithstablenoise
_version_	1725135134008541184

Approximations for a solution to stochastic heat equation with stable noise

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