Estimation of sojourn time distributions for cyclic semi-Markov processes in equilibrium

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

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Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

Journal of Applied Probability ◽

10.1017/s0021900200045903 ◽

1978 ◽

Vol 15 (03) ◽

pp. 531-542

Author(s):

Izzet Sahin

Keyword(s):

Markov Processes ◽

Sojourn Time ◽

Working Life ◽

Partial Coverage ◽

Sojourn Times ◽

Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

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Sojourn times in finite Markov processes

Journal of Applied Probability ◽

10.2307/3214379 ◽

1989 ◽

Vol 26 (4) ◽

pp. 744-756 ◽

Cited By ~ 75

Author(s):

Gerardo Rubino ◽

Bruno Sericola

Keyword(s):

Markov Process ◽

Asymptotic Behaviour ◽

Markov Processes ◽

Discrete Time ◽

Continuous Time ◽

Sojourn Time ◽

Sojourn Times ◽

Finite State ◽

Sojourn Time Distributions ◽

Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

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Sojourn times in finite Markov processes

Journal of Applied Probability ◽

10.1017/s0021900200027613 ◽

1989 ◽

Vol 26 (04) ◽

pp. 744-756 ◽

Cited By ~ 10

Author(s):

Gerardo Rubino ◽

Bruno Sericola

Keyword(s):

Markov Process ◽

Asymptotic Behaviour ◽

Markov Processes ◽

Discrete Time ◽

Continuous Time ◽

Sojourn Time ◽

Sojourn Times ◽

Finite State ◽

Sojourn Time Distributions ◽

Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

Download Full-text