Augmented truncation approximations of discrete-time Markov chains

✍ Scribed by Yuanyuan Liu

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 305 KB
• Volume: 38
• Category: Article
• ISSN: 0167-6377
• DOI: 10.1016/j.orl.2009.12.001

✦ Synopsis

Let P be a positive recurrent infinite transition matrix with invariant distribution π and (n) P be a truncated and arbitrarily augmented stochastic matrix with invariant distribution (n) π. We investigate the convergence (n) ππ → 0, as n → ∞, and derive a widely applicable sufficient criterion. Moreover, computable bounds on the error (n) ππ are obtained for polynomially and geometrically ergodic chains. The bounds become rather explicit when the chains are stochastically monotone.