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The Gillis–Domb–Fisher correlated random walk

Published online by Cambridge University Press:  14 July 2016

Anyue Chen  and
Eric Renshaw
Anyue Chen*
Affiliation:
University of Edinburgh
Eric Renshaw*
Affiliation:
University of Strathclyde
*
∗ Postal address: Department of Statistics, James Clerk Maxwell Building, King's Buildings, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK.
∗∗ Postal address: Department of Statistics and Modelling Science, Livingstone Tower, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK.
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Abstract

Correlated random walk models figure prominently in many scientific disciplines. Of fundamental importance in such applications is the development of the characteristic function of the n-step probability distribution since it contains complete information on the probability structure of the process. Using a simple algebraic lemma we derive the n-step characteristic function of the Gillis correlated random walk together with other related results. In particular, we present a new and simple proof of Gillis's conjecture, consider the generalization to the Gillis–Domb–Fisher walk, and examine the effect of including an arbitrary initial distribution.

Keywords

GILLIS WALKGILLIS–DOMB–FISHER WALKn-STEP DISTRIBUTIONCHARACTERISTICFUNCTIONMOMENTSRECURRENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 792 - 813
Copyright
Copyright © Applied Probability Trust 1992 

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