The secretary problem for a random walk

M. Hlynka; J. N. Sheahan

doi:10.1016/0304-4149(88)90104-4

The secretary problem for a random walk

M. Hlynka, J. N. Sheahan

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

12 Citations (Scopus)

Abstract

The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.

Original language	English
Pages (from-to)	317-325
Number of pages	9
Journal	Stochastic Processes and their Applications
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/0304-4149(88)90104-4
Publication status	Published - Jun 1988
Externally published	Yes

Keywords

optimal stopping
random walk
secretary problem

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10.1016/0304-4149(88)90104-4

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title = "The secretary problem for a random walk",

abstract = "The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.",

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AB - The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.

KW - optimal stopping

KW - random walk

KW - secretary problem

UR - https://www.scopus.com/pages/publications/0042407018

U2 - 10.1016/0304-4149(88)90104-4

DO - 10.1016/0304-4149(88)90104-4

M3 - Article

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VL - 28

SP - 317

EP - 325

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

The secretary problem for a random walk

Abstract

Keywords

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