The Burgers superprocess
type: Item
instance of: scholarly article
title: The Burgers superprocess
zbMATH Open document ID: 1117.60062
author: Guillaume Bonnet
author: Robert J. Adler
published in: Stochastic Processes and their Applications
publication date: 2007-02-19T00:00:00Z
review text: The authors define the Burgers superprocess to be the solution of the stochastic partial differential equation \[ \partial_t u=\partial_x^2 u -\lambda u \partial_x u +\gamma \sqrt{u} \dot{W} \] for \(u(t,x)\) with \(t\geq 0\) and \(x\in(-\infty,\infty)\), and \(\dot{W}(t,x)\) being space-time white noise. The limiting cases are the Burgers equation for \(\gamma=0\) and the super-Brownian motion for \(\lambda=0\). The existence of a weak solution is shown and the problem of uniqueness is discussed. In the method of proof the authors rely on spatial discretization in the spirit of the numerical method of lines and tightness arguments, in order to construct a solution. This solution is Hölder-continuous, positive, and dies out in finite time.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 5128007
zbMATH Keywords: Burgers equation
zbMATH Keywords: superprocess
zbMATH Keywords: stochastic partial differential equation
zbMATH Keywords: space-time white noise
zbMATH Keywords: numerical method of lines
MaRDI profile type: Publication
full work available at URL: j.spa.2006.06.004
OpenAlex ID: W2059894499
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DOI: 10.1016/J.SPA.2006.06.004
description: scientific article; zbMATH DE number 5128007