Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 1

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij (t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

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Quasi-stationary distributions in semi-Markov processes

Journal of Applied Probability ◽

10.2307/3211972 ◽

1970 ◽

Vol 7 (2) ◽

pp. 388-399 ◽

Cited By ~ 9

Author(s):

C. K. Cheong

Keyword(s):

Markov Process ◽

State Space ◽

Markov Processes ◽

Transition Probability ◽

Main Concern ◽

Initial State ◽

Stationary Distributions ◽

Semi Markov Process ◽

Image Position ◽

Semi Markov Processes

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij(t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

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Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes

Nonlinearly Perturbed Semi-Markov Processes - SpringerBriefs in Probability and Mathematical Statistics ◽

10.1007/978-3-319-60988-1_3 ◽

2017 ◽

pp. 37-66 ◽

Cited By ~ 4

Author(s):

Dmitrii Silvestrov ◽

Sergei Silvestrov

Keyword(s):

Markov Processes ◽

Asymptotic Expansions ◽

Hitting Times ◽

Semi Markov Processes

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Additional quasi-stationary distributions for semi-Markov processes

Journal of Applied Probability ◽

10.2307/3212336 ◽

1972 ◽

Vol 9 (3) ◽

pp. 671-676 ◽

Cited By ~ 3

Author(s):

David C. Flaspohler ◽

Paul T. Holmes

Keyword(s):

Markov Process ◽

Markov Processes ◽

Sufficient Conditions ◽

Initial State ◽

Stationary Distributions ◽

Absorbing State ◽

Semi Markov Process ◽

Image Position ◽

Semi Markov Processes

Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj(t) is the amount of time prior to time t spent in state j.The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.

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