Résumé
Nous montrons un théorème central limite et une estimée des grandes déviations pour les solutions d'équations différentielles stochastiques linéaires à coefficients markoviens. Ces résultats sont obtenus dans le cadre général des processus markoviens multiplicatifs. Ils s'appliquent alors par exemple au flot dérivé d'un flot stochastique sur une variété compacte et aux produits de matrices aléatoires en dépendance markovienne.
Summary
We show a central limit theorem and a law of large deviations for the solutions of linear stochastic differential equations with markovian coefficients under weak hypothesis. These results are obtained in the general set up of Markov Multiplicative Processes. They can thus be applied, for instance, to the derivative of a stochastic flow on a compact maniold and to the product of random matrices with markovian dependence.
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Bougerol, P. Théorèmes limite pour les systèmes linéaires à coefficients markoviens. Probab. Th. Rel. Fields 78, 193–221 (1988). https://doi.org/10.1007/BF00322018
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DOI: https://doi.org/10.1007/BF00322018