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March, 1976 Stopping a Sum During a Success Run
Thomas S. Ferguson
Ann. Statist. 4(2): 252-264 (March, 1976). DOI: 10.1214/aos/1176343405


Let $\{Z_i\}$ be i.i.d., let $\{\varepsilon_i\}$ be i.i.d. Bernoulli, independent of $\{Z_i\}$, let $T_0 = z$ and $T_n = \varepsilon_n(T_{n-1} + Z_n)$ for $n \geqq 1$. Under a moment condition, optimal stopping rules are found for stopping $T_n - nc$ where $c > 0$ (the cost model), and for stopping $\beta^nT_n$ where $0 < \beta < 1$ (the discount model). Special cases are treated in detail. The cost model generalizes results of N. Starr, and the discount model generalizes results of Dubins and Teicher.


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Thomas S. Ferguson. "Stopping a Sum During a Success Run." Ann. Statist. 4 (2) 252 - 264, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0324.62062
MathSciNet: MR408144
Digital Object Identifier: 10.1214/aos/1176343405

Primary: 62L15
Secondary: 60G40

Keywords: cost model , discount model , Optimal stopping rules , Principle of optimality

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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