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Convex large deviation rate functions under mixtures of linear transformations, with an application to ruin theory

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  • Nyrhinen, Harri

Abstract

Let X1,X2,... be a sequence of random vectors taking values in . Let be a random d'xd matrix which is independent of the process {Xn}. Suppose that {Xn} satisfies the large deviations upper or lower bounds with a convex rate function. Starting with this, we derive large deviations statements for the mixture . The case where is deterministic is studied in more detail in the framework of the Gärtner-Ellis theorem. The results are applied to a ruin problem.

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  • Nyrhinen, Harri, 2007. "Convex large deviation rate functions under mixtures of linear transformations, with an application to ruin theory," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 947-959, July.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:7:p:947-959
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    References listed on IDEAS

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