Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise release_lapg5osjbbexdliiujr64h3mhe

by Marta Sanz-Solé, André Süß

Released as a article .

2014  

Abstract

We consider the family of stochastic partial differential equations indexed by a parameter ∈(0,1], Lu^(t,x) = σ(u^(t,x))Ḟ(t,x)+b(u^(t,x)), (t,x)∈(0,T]× with suitable initial conditions. In this equation, L is a second-order partial differential operator with constant coefficients, σ and b are smooth functions and Ḟ is a Gaussian noise, white in time and with a stationary correlation in space. Let p^_t,x denote the density of the law of u^(t,x) at a fixed point (t,x)∈(0,T]×. We study the existence of _↓ 0^2 p^_t,x(y) for a fixed y∈. The results apply to a class of stochastic wave equations with d∈{1,2,3} and to a class of stochastic heat equations with d>1.
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Date   2014-07-18
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arXiv  1312.1257v2
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