Negative binomial sums of random variables and discounted reward processes

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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.

Original languageEnglish (US)
Pages (from-to)589-599
Number of pages11
JournalJournal of Applied Probability
Volume35
Issue number3
DOIs
StatePublished - Sep 1998

Keywords

  • Markov decision processes
  • Reward processes
  • Sums of random variables

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