On the average of a random walk

Karl Grill

Statistics & Probability Letters, 1988, vol. 6, issue 5, 357-361

Abstract: Let {Sn, n [epsilon] N)} be a simple random walk and denote by An its time average: An = (S1+ ...+Sn)/n. We give an integral test for the lower bound on An, thus giving an affirmative answer to a conjecture of P. Erdös (private communication) that An will return to a fixed region around the origin infinitely often with probability 1 in 1 dimension whereas in 2 or more dimensions it will return only finitely many times.

Keywords: random; walk; recurrence; strong; laws (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (3)

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