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

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.

MoreLess

Year of publication:	2007
Authors:	Nyrhinen, Harri
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 117.2007, 7, p. 947-959
Publisher:	Elsevier
Keywords:	Large deviations theory Convex rate function Gartner-Ellis theorem Ruin probability

More details

Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008874676