Invariant measures of stochastic partial differential equations and conditioned diffusions

Maria G. Reznikoff, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review

Abstract

This work establishes and exploits a connection between the invariant measure of stochastic partial differential equations (SPDEs) and the law of bridge processes. Namely, it is shown that the invariant measure of ut = uxx + f(u) + √2ε η(x,t), where η(x,t) is a space-time white-noise, is identical to the law of the bridge process associated to dU = a(U) dx + √εdW (x), provided that a and f are related by εa″ (u) + 2a′ (u) a(u) = -2f(u), u ∈ ℝ. Some consequences of this connection are investigated, including the existence and properties of the invariant measure for the SPDE on the line, x ∈ ℝ.

Original languageEnglish (US)
Pages (from-to)305-308
Number of pages4
JournalComptes Rendus Mathematique
Volume340
Issue number4
DOIs
StatePublished - Feb 15 2005

ASJC Scopus subject areas

  • Mathematics(all)

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