Small perturbations in a hyperbolic stochastic partial differential equation

David Márquez-Carreras and Marta Sanz-Solé

Stochastic Processes and their Applications, 1997, vol. 68, issue 1, 133-154

Abstract: We study the existence and properties of the density for the law of the solution to a nonlinear hyperbolic stochastic partial differential equation, driven by a two-parameter white noise. We also analyze the asymptotic behavior of the density for the law of the solution to the equation obtained by perturbing the noise. Under unrestricted Hörmander's-type conditions on the coefficients, we establish Varadhan's estimates.

Keywords: Stochastic; partial; differential; equations; Malliavin; calculus; Large; deviations; Density; estimates (search for similar items in EconPapers)
Date: 1997
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