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A Laplace Principle for a Stochastic Wave Equation in Spatial Dimension Three

In: Stochastic Analysis 2010

Author

Listed:
  • Víctor Ortiz-López

    (Universitat de Barcelona, Facultat de Matemàtiques)

  • Marta Sanz-Solé

    (Universitat de Barcelona, Facultat de Matemàtiques)

Abstract

We consider a stochastic wave equation in spatial dimension three, driven by a Gaussian noise, white in time and with a stationary spatial covariance. The free terms are non-linear with Lipschitz continuous coefficients. Under suitable conditions on the covariance measure, Dalang and Sanz-Solé (“Memoirs of the AMS, 199, 931, 2009”) have proved the existence of a random field solution with Hölder continuous sample paths, jointly in both arguments, time and space. By perturbing the driving noise with a multiplicative parameter ε ∈ ]0, 1], a family of probability laws corresponding to the respective solutions to the equation is obtained. Using the weak convergence approach to large deviations developed in (“Dupuis and Ellis, A weak convergence approach to the theory of large deviations, Wiley, 1997”), we prove that this family satisfies a Laplace principle in the Hölder norm.

Suggested Citation

  • Víctor Ortiz-López & Marta Sanz-Solé, 2011. "A Laplace Principle for a Stochastic Wave Equation in Spatial Dimension Three," Springer Books, in: Dan Crisan (ed.), Stochastic Analysis 2010, pages 31-49, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-15358-7_3
    DOI: 10.1007/978-3-642-15358-7_3
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