Pathwise analysis and parameter estimation for the stochastic Burgers equation

We analyze the solution to the stochastic Burgers equation with additive space-time white noise. We show that this solution can be expressed as a sum of a random field that solves the stochastic heat equation with additive space-time white noise and a more regular random field. We apply these result...

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Bibliographic Details
Published inBulletin des sciences mathématiques Vol. 170; p. 102995
Main Authors Assaad, Obayda, Tudor, Ciprian A.
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.09.2021
Elsevier
Subjects
Mathematics
Multiple Wiener-Itô integrals
p-variation
Parameter estimation
Stochastic Burgers equation
Stochastic heat equation
Strong consistency
60G35
Parameter estimation
p-variation
Stochastic Burgers equation
Multiple Wiener-Itô integrals
Strong consistency
Stochastic heat equation
60H07
60H15
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Summary:We analyze the solution to the stochastic Burgers equation with additive space-time white noise. We show that this solution can be expressed as a sum of a random field that solves the stochastic heat equation with additive space-time white noise and a more regular random field. We apply these results in order to estimate the drift parameter of solution to the Burgers equation by exploiting the behavior of the p-variations of the solution in time and in space.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2021.102995