Pathwise analysis and parameter estimation for the stochastic Burgers equation
type: Item
instance of: scholarly article
title: Pathwise analysis and parameter estimation for the stochastic Burgers equation
zbMATH Open document ID: 1479.60119
author: Obayda Assaad
author: Ciprian A. Tudor
published in: Bulletin des Sciences Mathématiques
publication date: 2021-07-08T00:00:00Z
review text: The solution to the stochastic Burgers equation with additive space-time white noise is analyzed in this work. The authors have contributed a first step towards the statistical inference of the stochastic Burgers equation. That is, they aim at estimating the drift parameter based on the discrete observation of the solution to stochastic Burgers equation on a finite interval. The estimators are constructed via the \(p\)-variations of the solution. The authors show that the solution to the Burgers equation admits a quadratic variation in space and a quartic variation in time and using this fact, they obtain the asymptotic properties (strong consistency, approximation error in \(L^p\)-norm) of the estimators. The main idea behind the proofs is to decompose the solution to stochastic Burgers equation into a sum of two stochastic processes, one of them coinciding with the solution to the linear stochastic heat equation (whose properties are well-known) and a second term which contains the nonlinear coefficient. The authors 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.
reviewed by: Manil T. Mohan
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60H40
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 7369575
zbMATH Keywords: parameter estimation
zbMATH Keywords: stochastic Burgers equation
zbMATH Keywords: stochastic heat equation
zbMATH Keywords: \(p\)-variation
zbMATH Keywords: multiple Wiener-Itô integrals
zbMATH Keywords: strong consistency
MaRDI profile type: Publication
full work available at URL: j.bulsci.2021.102995
OpenAlex ID: W3162529224
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DOI: 10.1016/J.BULSCI.2021.102995
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description: scientific article; zbMATH DE number 7369575