Sharp upper bound on the almost-sure exponential behavior of a stochastic parabolic partial differential equation

Rene A. Carmona, Frederi G. Viens, S. A. Molchanov

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

Using a Gaussian estimate, we prove an upper bound on the almost-sure large time exponential growth of the solution to the parabolic Anderson model {equation presented} on the lattice Zd when the potential V(t} x) is a mean zero Gaussian field that is white in time and homogeneous in space. As the diffusivity parameter K tends to 0, our upper bound is of the same order as the lower bound given by Carmona and Molchanov in [2].

Original languageEnglish (US)
Pages (from-to)43-49
Number of pages7
JournalRandom Operators and Stochastic Equations
Volume4
Issue number1
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability

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