euclid.jap.1261670699

1 however the variances of the total discounted

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Unformatted text preview: ing randomized stationary and switching stationary policies [2, Theorem 5.1]. However, the variances of the total discounted rewards for the policies can be different. In addition, they may depend on the definition of discounting. Received 6 July 2009; revision received 5 October 2009. ∗ Postal address: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA. ∗∗ Email address: eugene.feinberg@sunysb.edu ∗∗∗ Email address: jun.fei@sunysb.edu 1209 1210 E. A. FEINBERG AND J. FEI 2. Main result Let ( , F , P) be a probability space with a filtration Ft , t ∈ [0, ∞), where Fs ⊆ Ft ⊆ F for all 0 ≤ s < t < ∞. Consider a nondecreasing sequence of stopping times Tn , n = 1, 2, . . . . Let Ft . F∞ = t ∈[0,∞) We consider an Ft -adapted stochastic process rt , t ∈ [0, ∞), and an FTn -adapted stochastic sequence Rn , n = 1, 2, . . . . The process rt can be interpreted as the reward rate at time t . In addition, a lump sum Rn is collected at time Tn . There are two n...
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This note was uploaded on 02/02/2014 for the course AMS 507 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.

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