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M. Ait Ouahra, M. Eddahbi, E. Lakhel

Large deviations and functional law for solutions of hyperbolic stochastic partial differential equations

Keywords: Large deviations, hyperbolic stochastic partial differential equations, twoparameter martingales, functional law of the iterated logarithms

In this paper, we derive large deviation estimates of Freidlin–Wentzell for solutions of hyperbolic stochastic partial differential equation. This result generalizes those of Doss and Dozzi (1987), N’zi (1994) and Eddahbi (1997) to a large class of stochastic differential equations involving a two–parameter Wiener process. These solutions are obtained by small perturbations of the noise. As an application we give a functional law of the iterated logarithms.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 11, 12/2003
Pages: 307 - 332

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