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

Harri Nyrhinen

Stochastic Processes and their Applications, 2007, vol. 117, issue 7, 947-959

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.

Keywords: Large; deviations; theory; Convex; rate; function; Gartner-Ellis; theorem; Ruin; probability (search for similar items in EconPapers)
Date: 2007
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