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Optimal stopping of observations in problems of control of random walks. (Russian) Zbl 0713.60055

The paper deals with an analytical and a numerical method for the following special problem of optimal control for the random walk. Let \(\{\xi_ i^ j\}\), \(i=1,2,...,N\), \(j=1,2,..\). be a doubly indexed sequence of i.i.d. random variables with continuous uniform distribution on [0,1]. For successive j one can choose an observation \(\xi^ j_{i(j)}\) [like in the full information best choice problem described for example in J. P. Gilbert and F. Mosteller, J. Am. Stat. Assoc. 61, 35-73 (1966)] and go to investigate the next subsequence \(\{\xi_ i^{j+1}\}\), \(i=1,2,...,N\). The strategy of choice is searched to have \(\sum^{r-1}_{j=1}\xi^ j_{i(j)}<X\leq \sum^{r}_{j=1}\xi^ j_{i(j)}\) with minimal \(E\tau\), where X is a given positive number.
Reviewer: K.Szajowski

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
91A15 Stochastic games, stochastic differential games
60G50 Sums of independent random variables; random walks
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