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Reward processes with nonlinear reward functions

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

A. Reza Soltani
A. Reza Soltani*
Affiliation:
Shiraz University
*
∗ Postal address: Department of Statistics, College of Sciences, Shiraz University, Shiraz 71454, Iran. This research was supported by the Institute for Studies in Theoretical Physics and Mathematics.
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Abstract

Based on a semi-Markov process J(t), t ≧ 0, a reward process Z(t), t ≧ 0, is introduced where it is assumed that the reward function, p(k, x) is nonlinear; if the reward function is linear, i.e. ρ (k, x) = kx, the reward process Z(t), t ≧ 0, becomes the classical one, which has been considered by many authors. An explicit formula for E(Z(t)) is given in terms of the moments of the sojourn time distribution at t, when the reward function is a polynomial.

Keywords

SEMI-MARKOV PROCESSESREWARD PROCESSESLAPLACE TRANSFORM

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K05: Renewal theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1011 - 1017
Copyright
Copyright © Applied Probability Trust 1996 

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References

[1] Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123–187.Google Scholar
[2] Çinlar, E. (1975) Markov renewal theory: A survey. Management Sci. 21, 727–752.Google Scholar
[3] Masuda, Y. and Sumita, U. (1991) A multivariate reward process defined on a semi-Markov process and its first passage time distributions. J. Appl. Prob. 28, 360–373.CrossRefGoogle Scholar
[4] McLean, R. A. and Neuts, M. F. (1967) The integral of a step function defined on a semi-Markov process. SIAM J. Appl. Math. 15, 726–737.Google Scholar
[5] Sumita, U. and Masuda, Y. (1987) An alternative approach to the analysis of finite semi-Markov processes. Stoch. Models 3, 67–78.Google Scholar