Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem

Rene A. Carmona, Leonid Koralov, Stanislav Molchanov

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We consider the Stochastic Partial Differential Equation [equation presented] The potential is assumed to be Gaussian white noise in time, stationary in space. We obtain the asymptotics of the almost sure Lyapunov exponent γ(k) for the solution as k→0. Namely γ(k)∼c0/ln(1/ k), where the constant C0 is determined by the correlation function of the potential.

Original languageEnglish (US)
Pages (from-to)77-86
Number of pages10
JournalRandom Operators and Stochastic Equations
Volume9
Issue number1
DOIs
StatePublished - Jan 2001

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability

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