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Negative binomial sums of random variables and discounted reward processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

William L. Cooper
William L. Cooper*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta GA 30332, USA. Email address: billcoop@isye.gatech.edu
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Abstract

Given a sequence of random variables (rewards), the Haviv–Puterman differential equation relates the expected infinite-horizon λ-discounted reward and the expected total reward up to a random time that is determined by an independent negative binomial random variable with parameters 2 and λ. This paper provides an interpretation of this proven, but previously unexplained, result. Furthermore, the interpretation is formalized into a new proof, which then yields new results for the general case where the rewards are accumulated up to a time determined by an independent negative binomial random variable with parameters k and λ.

Keywords

Sums of random variablesreward processesMarkov decision processes

MSC classification

Primary: 60G99: None of the above, but in this section
Secondary: 90C40: Markov and semi-Markov decision processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 589 - 599
Copyright
Copyright © Applied Probability Trust 1998 

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References

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