Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients

[摘要] In this paper, we deal with the real stochastic difference equation Yn+1 = a(n) Y-n + b(n), n is an element of Z where the sequence (a(n)) is a finite state space Markov chain. By means of the renewal theory, we give a precise description of the situation where the tail of its stationary solution exhibits power law behavior. (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2005-12-01

[关键词] stochastic difference equation;Markov-switching auto-regression;Markov chains;renewal theory;non-negative matrices;spectral radius;random walk;ladder heights