Variations of the elephant random walk

In the classical simple random walk the steps are independent, that is, the walker has no memory. In contrast, in the elephant random walk, which was introduced by Schütz and Trimper [19] in 2004, the next step always depends on the whole path so far. Our main aim is to prove analogous results when...

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Bibliographic Details
Published inJournal of applied probability Vol. 58; no. 3; pp. 805 - 829
Main Authors Gut, Allan, Stadtmüller, Ulrich
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2021
Applied Probability Trust
Subjects
asymptotic (non)normality
difference equation
Elephant random walk
Elephants
Expected values
law of large numbers
Markov chain
method of moments
Original Article
Phase transitions
Random variables
Random walk
Research Papers
difference equation
Markov chain
60J10
law of large numbers
asymptotic (non)normality
60G50
method of moments
Elephant random walk
60F05
60F15
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Summary:In the classical simple random walk the steps are independent, that is, the walker has no memory. In contrast, in the elephant random walk, which was introduced by Schütz and Trimper [19] in 2004, the next step always depends on the whole path so far. Our main aim is to prove analogous results when the elephant has only a restricted memory, for example remembering only the most remote step(s), the most recent step(s), or both. We also extend the models to cover more general step sizes.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0021-9002
1475-6072
1475-6072
DOI:10.1017/jpr.2021.3