An asymptotic theory for randomly forced discrete nonlinear heat equations

Mohammud Foondun, Davar Khoshnevisan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study discrete nonlinear parabolic stochastic heat equations of the form, un+1(x)-un(x) = (Lun)(x)+ σ(u n(x))ζn(x), for n ∈ Z+ and x ∈ Zd, where ζ := {ζn(x)} n≥0,x∈Zd denotes random forcing and L the generator of a random walk on Zd. Under mild conditions, we prove that the preceding stochastic PDE has a unique solution that grows at most exponentially in time. And that, under natural conditions, it is "weakly intermittent." Along the way, we establish a comparison principle as well as a finite support property.

Original languageEnglish
Pages (from-to)1042-1060
Number of pages19
JournalBernoulli
Volume18
Issue number3
Early online date28 Jun 2012
DOIs
Publication statusPublished - 31 Aug 2012
Externally publishedYes

Keywords

  • intermittency
  • stochastic heat equations

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