An extremal problem related to probability

Autor:	Dennis C. Russell, Jürg Rätz
Rok vydání:	1987
Předmět:	Combinatorics Polynomial Applied Mathematics General Mathematics Discrete Mathematics and Combinatorics Maximization Random walk Value (mathematics) Mathematics
Zdroj:	Aequationes Mathematicae. 34:316-324
ISSN:	1420-8903 0001-9054
DOI:	10.1007/bf01830681
Popis:	We consider a walk from a stateA1 to a stateAn+1 in which the probability of remaining atA i isp i , and the probability of progressing fromA i toAi+1 is 1 −p i . The probabilityW nk of reachingAn+1 fromA1 in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp1,⋯,p n . We determine the maximum value ofW nk and the (unique) choice (p1,⋯,p n ) for which this extremum occurs.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::74fbbb62caa15058afeb67d43245c43e https://doi.org/10.1007/bf01830681 Zobrazit plný text záznamu Full text from SpringerLink