1955/10/01 by J. Gillis · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Stochastic processes and statistical mechanics #Diffusion and Search Dynamics #Scientific Research and Discoveries
paper · doi:10.1017/s0305004100030711
ABSTRACT Random 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 2 n steps. This latter function is evaluated asymptotically for the cases d = 1 and d = an even integer.