A Characterisation of Transient Random Walks on Stochastic Matrices with Dirichlet Distributed Limits. (June 2014)

• Record Type: Journal Article
• Authors: McKinlay, S.
• Is Part Of: Journal of applied probability. Volume 51:Number 2(2014)
• Page Start: 542
• Page End: 555
• Publication Date: 2014-06
• Subjects: Products of random matrices, -- Dirichlet distribution, -- limit distribution, -- Markov chain, -- random exchange model, -- random nested simplices, -- service networks with polling; 60J05, -- 60B20, -- 60F99, -- 60J20; 519.2
• DOI: 10.1239/jap/1402578642
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : We characterise the class of distributions of random stochastic matrices X with the property that the products X ( n ) X ( n − 1) · · · X (1) of independent and identically distributed copies X ( k ) of X converge almost surely as n → ∞ and the limit is Dirichlet distributed. This extends a result by Chamayou and Letac (1994) and is illustrated by several examples that are of interest in applications.