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Journal of Theoretical Probability

, Volume 9, Issue 4, pp 863–901 | Cite as

The law of the solution to a nonlinear hyperbolicSPDE

  • Carles Rovira
  • Marta Sanz-Solé
Article

Abstract

Let {\(\dot W\) s,t ,(s,t∈ℝ + 2 } be a white noise on ℝ + 2 . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.

Key Words

HyperbolicSPDE's strong and weak solution Malliavin calculus large deviations 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Carles Rovira
    • 1
  • Marta Sanz-Solé
    • 1
  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

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