Monotone infinite stochastic matrices and their augmented truncations

Diana Gibson and E. Seneta

Stochastic Processes and their Applications, 1987, vol. 24, issue 2, 287-292

Abstract: Let P be a positive-recurrent, stochastically monotone, stochastic matrix on the positive integers, with stationary vector [pi]. Let (n)P be an (n x n) stochastic matrix where 1, and (n)P is the (n x n) northwest corner truncation of P, and suppose (n)[pi] is any stationary vector of (n)P. We show that (n)[pi] --> [pi] elementwise as n --> [infinity]. One corollary is the convergence to [pi] of quasistationary distributions of the (n)P. Another is that the conditions on P itself can be relaxed to domination of P by a positive-recurrent, stochastically monotone matrix R.

Keywords: stochastically; monotone; truncations; quasi-stationary (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (7)

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