Relative stability and weak convergence in non-decreasing stochastically monotone Markov chains. (1991)

• Record Type: Journal Article
• Authors: Todorovic, P.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 4:Number 4(1991)
• Page Start: 293
• Page End: 303
• Publication Date: 1991
• Subjects: Markov chain -- stochastic monotonicity -- Markov renewal process -- relative stability -- weak convergence; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953391000229
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Let { ξ n } be a non-decreasing stochastically monotone Markov chain whose transition probability Q ( ., . ) has Q ( x, { x } ) = β ( x ) > 0 for some function β ( . ) that is non-decreasing with β ( x ) ↑ 1 as x → + ∞, and each Q ( x, . ) is non-atomic otherwise. A typical realization of { ξ n } is a Markov renewal process { ( X n, T n ) }, where ξ j = X n, for T n consecutive values of j, T n geometric on { 1, 2, … } with parameter β ( X n ) . Conditions are given for X n, to be relatively stable and for T n to be weakly convergent.