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A note on the recurrence of a correlated random walk. (English) Zbl 0535.60060

A particle is initially situated at the origin of an infinite square lattice and subsequently moves in unit steps parallel to either axis. The first step is equally probable to be in any of the four permissible directions. Subsequent step movements relative to the previous step direction, \(\uparrow\) say, are given by \(P(\uparrow)=p\); \(P(\downarrow)=q\); \(P(\to)=P(\theta)=r\) with \(p+q+2r=1\). A non-analytical proof of recurrence of this correlated random walk is obtained by embedding the described random walk in a ”constrained” random walk of alternating step directions with variable step length.
Reviewer: F.T.Bruss

MSC:

60G50 Sums of independent random variables; random walks
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