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Erschienen in:
2021 | OriginalPaper | Buchkapitel
Controlled Random Walk: Conjecture and Counter-Example
verfasst von : Alexey B. Piunovskiy
Erschienen in: Modern Trends in Controlled Stochastic Processes:
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Abstract
In this paper we investigate the following conjecture about the random walk on the positive integer lattice, starting from a large point \(i>0\) and up to the absorption at negative points: on the first steps, one has to maximize the expected reward coming from passing through one point on the lattice. Under appropriate conditions, this conjecture is true. The counter-example shows that sometimes it is not valid.