Windings of spherically symmetric random walks via Brownian embedding

Claude Bélisle

Statistics & Probability Letters, 1991, vol. 12, issue 4, 345-349

Abstract: Let X1, X2, X3,... be a sequence of i.i.d. 2-valued random variables with a spherically symmetric distribution. Let (Sn; n[greater-or-equal, slanted]0) be its sequence of partial sums and let ([phi](n); n[greater-or-equal, slanted]0) be its winding sequence. Assuming only a mild moment condit show, via Brownian embedding, that 2[phi](n)/log n converges in distribution to a standard hyperbolic secant distribution.

Keywords: Random; walks; Brownian; motion; windings; asymptotic; distribution (search for similar items in EconPapers)
Date: 1991
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