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Large Deviations of Solutions of Hyperbolic SPDE's in the Hölder Norm

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Abstract

In this paper, we prove the large deviations principle for solutions of a hyperbolic stochastic partial differential equation, in the Hölder topology of index α for all 0 ≤ α < \(\frac{1}{2}\). This result generalizes those in [5] and [10] to the Hölder norm, and the result in [3] for solutions of a class fo stochastic differential equations involving a two-parameter Wiener process. These solutions are obtained by small perturbations of the noise.

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  1. Départment de Mathématiques et d'informatiques, Université Cadi Ayyad Faculté des Sciences et Techniques B.P. 618, Marrackech, Moroc

    M'hemed Eddahbi

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  1. M'hemed Eddahbi
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Eddahbi, M. Large Deviations of Solutions of Hyperbolic SPDE's in the Hölder Norm. Potential Analysis 7, 517–537 (1997). https://doi.org/10.1023/A:1008684228912

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