Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T04:20:06.170Z Has data issue: false hasContentIssue false
  • English
  • Français

Sequential limits in Markov set-chains

Published online by Cambridge University Press:  14 July 2016

D. J. Hartfiel
D. J. Hartfiel*
Affiliation:
Texas A&M University
*
∗ Postal address: Mathematics Department, Texas A&M University, College Station, TX 77843–3368, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let T be a non-empty subset of η X n stochastic matrices. Define The sequence T1, T2, · ·· is called a Markov set-chain. An important problem in this area is to determine when such a set-chain converges. This paper gives a notion of a sequential limiting set and shows how it can be used to obtain a result on set-chain convergence.

Keywords

PRODUCTS OF STOCHASTIC MATRIX SETSCONVERGENCE IN THE HAUSDORFF METRICNON-HOMOGENEOUS MARKOV CHAINSWEAKLY ERGODIC
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 910 - 913
Copyright
Copyright © Applied Probability Trust 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Hartfiel, D. J. (1981) On the limiting set of stochastic products xA1Ak. Proc. Amer. Math. Soc. 81, 201–206.Google Scholar
[2] Hartfiel, D. J. (1987) Computing limits of convex sets of distribution vectors xA1Ak. J. Statist. Comput. Simul. 27, 1–15.10.1080/00949658708810998Google Scholar
[3] Hartfiel, D. J. (1991) Component bounds on Markov set-chain limiting sets. J. Statist. Comput. Simul. 38, 15–24.10.1080/00949659108811316Google Scholar
[4] Moore, R. L. (1962) Foundations of Point Set Theory. American Mathematical Society Colloquium Publication, XIII, American Mathematical Society, Providence RI.Google Scholar
[5] Seneta, E. (1973) Non-negative Matrices. Wiley, New York.Google Scholar
[6] Whyburn, G. T. (1942) Analytic Topology, American Mathematical Society Colloquium Publication XXVIII, Americal Mathematical Society, Providence RI.10.1090/coll/028Google Scholar