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A CLOSED FORM FOR THE DENSITY FUNCTIONS OF RANDOM WALKS IN ODD DIMENSIONS

Part of: Stochastic processes

Published online by Cambridge University Press:  02 October 2015

JONATHAN M. BORWEIN  and
CORWIN W. SINNAMON
JONATHAN M. BORWEIN
Affiliation:
CARMA, University of Newcastle, NSW 2303, Australia email [email protected]
CORWIN W. SINNAMON*
Affiliation:
University of Waterloo, Ontario N2L 3G1, Canada email [email protected]
*
✉[email protected]
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Abstract

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We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.

Keywords

short random walksgeneralised hypergeometric functionsBessel integrals

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 33C20: Generalized hypergeometric series, $_pF_q$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 330 - 339
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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