Journal of Applied Probability

Negative binomial sums of random variables and discounted reward processes

William L. Cooper

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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.

Article information

Source
J. Appl. Probab. Volume 35, Number 3 (1998), 589-599.

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.jap/1032265207

Digital Object Identifier
doi:10.1239/jap/1032265207

Mathematical Reviews number (MathSciNet)
MR1659512

Zentralblatt MATH identifier
0918.60034

Subjects
Primary: 60G99: None of the above, but in this section
Secondary: 90C40: Markov and semi-Markov decision processes

Keywords
Sums of random variables reward processes Markov decision processes

Citation

Cooper, William L. Negative binomial sums of random variables and discounted reward processes. J. Appl. Probab. 35 (1998), no. 3, 589--599. doi:10.1239/jap/1032265207. https://projecteuclid.org/euclid.jap/1032265207


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