Abstract
ABSTRACTRandom walk on a d-dimensional lattice is investigated such that, at any stage, the probabilities of the step being in the various possible directions depend upon the direction of the previous step. The motion may be characterized by a generating function which is here derived. The generating function is then used to obtain some general properties of the walk. Certain special cases are considered in greater detail. The existence of recurrent points is investigated in particular, and the probability of returning to the origin after 2n steps. This latter function is evaluated asymptotically for the cases d = 1 and d = an even integer.
Publisher
Cambridge University Press (CUP)
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