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

Víctor Ortiz-López () and Marta Sanz-Solé ()
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Víctor Ortiz-López: Universitat de Barcelona, Facultat de Matemàtiques
Marta Sanz-Solé: Universitat de Barcelona, Facultat de Matemàtiques

A chapter in Stochastic Analysis 2010, 2011, pp 31-49 from Springer

Abstract: 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.

Keywords: Large deviation principle; Stochastic partial differential equations; AMS Subject Classification: 60H15; 60F10; Waveequation (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-15358-7_3

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DOI: 10.1007/978-3-642-15358-7_3

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