Almost-sure exponential behavior of a stochastic anderson model with continuous space parameter

We study the almost-sure large time exponential growth of the solution to a linear stochastic parabolic equation with continuous space parameter, and a Gaussian-correlated potential that is white noise in time and homogeneous in space. We use the evolution form of that equation,for which existence a...

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Bibliographic Details
Published inStochastics and stochastics reports Vol. 62; no. 3-4; pp. 251 - 273
Main Authors Carmona, René.A., Viens, Frederi G.
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.01.1998
Subjects
AMS Subject Classification
Gaussian estimates
Lyapunov exponent
Primary: 60H15
Secondary: 60G17
spatial discretization
stochastic Feynman-Kac formulastochastic evolution equation
Stochastic partial differential equation
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ISSN1045-1129
DOI10.1080/17442509808834135

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Summary:We study the almost-sure large time exponential growth of the solution to a linear stochastic parabolic equation with continuous space parameter, and a Gaussian-correlated potential that is white noise in time and homogeneous in space. We use the evolution form of that equation,for which existence and uniqueness are known. We establish a Feynman-Kac formula for the solution. By using a method of discretization of time and space, we prove that for small diffusion parameter κ, there is a deterministic constant c such that almost surely
ISSN:1045-1129
DOI:10.1080/17442509808834135