, Volume 156, Issue 3-4, pp 593-612,
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Date: 12 Jun 2012

Tail homogeneity of invariant measures of multidimensional stochastic recursions in a critical case

Abstract

We consider the stochastic recursion \({X_{n+1} = M_{n+1}X_{n} + Q_{n+1}, (n \in \mathbb{N})}\) , where \({Q_n, X_n \in \mathbb{R}^d }\) , M n are similarities of the Euclidean space \({ \mathbb{R}^d }\) and (Q n , M n ) are i.i.d. We study asymptotic properties at infinity of the invariant measure for the Markov chain X n under assumption \({\mathbb{E}{[\log|M|]}=0}\) i.e. in the so called critical case.

This research project has been partially supported by MNiSW grant N N201 610740 and also by FWF grant FWF-P19115-N18.