Moments of Absorption Time for a Conditioned Random Walk
- 1 February 1979
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 60 (1) , 83-90
- https://doi.org/10.1002/sapm197960183
Abstract
A random walk on the set of integers {0,1,2,...,a} with absorbing barriers at 0 and a is considered. The transition times from the integers z (0<z<a) are random variables with finite moments. The nth moment of the time to absorption at a, Dz,n, conditioned on the walk starting at z and being absorbed at a, is discussed, and a difference equation with boundary values and initial values for Dz,n is given. It is solved in several special cases. The problem is motivated by questions from biology about tumor growth and multigene evolution which are discussed.Keywords
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