科研之友
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摘要
Let P be the transition matrix of a positive recurrent Markov chain on the integers with invariant probability vector pi(T), and let ((n))(P) over tilde P be a stochastic matrix, formed by augmenting the entries of the (n + 1) x (n + 1) northwest corner truncation of P arbitrarily, with invariant probability vector ((n))pi(T). We derive computable V -norm bounds on the error between pi(T) and ((n))pi(T) in terms of the perturbation method from three different aspects: the Poisson equation, the residual matrix, and the norm ergodicity coefficient, which we prove to be effective by showing that they converge to 0 as n tends to infinity under suitable conditions. We illustrate our results through several examples. Comparing our error bounds with the ones of Tweedie (1998), we see that our bounds are more applicable and accurate. Moreover, we also consider possible extensions of our results to continuous-time Markov chains.
- 出版日期2018-6
- 单位中南大学
