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Some general results on random walks, with genetic applications

Published online by Cambridge University Press:  09 April 2009

P. A. P. Moran
P. A. P. Moran
Affiliation:
Institute of Advanced Studies, The Australian National University, Canbera
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Consider a random Markovian process in which the state of the system is defined by a random variable which can take the finite set of values i=0, 1, …, N, and which is such that transition can only occur from any state i to the two nearest states i+1. This restriction brings about an essential simplification of the theory for the basic reason that in order for the system to move from i to state j (i < j say) it must first move to i+1, then i+2 and so on until it reaches j. From this it follows that the first passage distribution from i to j is the convolution of the first passage distributions from i to i+l, i+l to i+2,…, j—l to j each of which is comparatively easy to find.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 4 , November 1963 , pp. 468 - 479
Copyright
Copyright © Australian Mathematical Society 1963

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