Stability index for products of random transformations

Abstract

The paper considers stability and instability properties of the Markov chain generated by the composition of an i.i.d. sequence of random transformations. The transformations are assumed to be either linear mappings or else mappings which can be well approximated near 0 by linear mappings. The main results concern the risk probabilities that the Markov chain enters or exits certain balls centered at 0. An application is given to the probability of extinction in a model from population dynamics.

Identifiers

DOI

10.1239/aap/1035228203

Citations and references