Relative stability and weak convergence in non-decreasing stochastically monotone Markov chains

P. Todorovic

International Journal of Stochastic Analysis, 1991, vol. 4, 1-11

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.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:560172

DOI: 10.1155/S1048953391000229

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