Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 4, Pages 293-303
Relative stability and weak convergence in non-decreasing
stochastically monotone Markov chains
University of California, Department of Statistics and Applied Probability, Santa Barbara, CA, USA
Received 1 January 1991; Revised 1 June 1991
Copyright © 1991 P. Todorovic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a non-decreasing stochastically monotone Markov
chain whose transition probability has for
some function that is non-decreasing with as , and
each is non-atomic otherwise. A typical realization of is a
Markov renewal process , where , for consecutive
values of , geometric on with parameter .
Conditions are given for , to be relatively stable and for to be