An extremal problem related to probability |
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Authors: | Jürg Rätz Dennis Russell |
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Affiliation: | (1) Mathematisches Institut der Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland;(2) Department of Mathematics, York University, M3J 1P3 Downsview, Ont., Canada |
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Abstract: | Summary We consider a walk from a stateA1 to a stateAn+1 in which the probability of remaining atAi ispi, and the probability of progressing fromAi toAi+1 is 1 –pi. The probabilityWnk of reachingAn+1 fromA1 in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp1,,pn. We determine the maximum value ofWnk and the (unique) choice (p1,,pn) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday |
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Keywords: | Primary 26C05 Secondary 60C05, 39A70 |
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