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Biometrika 1959 46(1-2):30-35; doi:10.1093/biomet/46.1-2.30
© 1959 by Biometrika Trust
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A RANDOM WALK IN WHICH THE STEPS OCCUR RANDOMLY IN TIME

A. MERCER * and C. S. SMITH

Atomic Weapons Research Establishment Aldermaston
National Coal Board London

The steps of a one-dimensional random walk are positive and occur randomly in time at a fixed mean rate. The sizes of the steps are independent and the size of each step has the same given probability distribution. The distribution of the time to reach a fixed barrier is obtained and approximations to its moments are derived. The results are extended to the case in which the barrier and the random walk process converge at a constant rate.


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