Windings of spherically symmetric random walks via Brownian embedding

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Abstract

Let X1, X2, X3,… be a sequence of i.i.d. R2-valued random variables with a spherically symmetric distribution. Let (Sn; n⩾0) be its sequence of partial sums and let (φ(n); n⩾0) be its winding sequence. Assuming only a mild moment condit show, via Brownian embedding, that 2φ(n)/log n converges in distribution to a standard hyperbolic secant distribution.

References (6)

  • C. Bélisle

    Windings of random walks

    Ann. Probab.

    (1989)
  • M.A. Berger

    The random walk winding number problem: convergence to a diffusion process with excluded area

    J. Phys. A Math. Gen.

    (1987)
  • M.A. Berger et al.

    On the winding number problem with finite steps

    Adv. Appl. Probab.

    (1988)
There are more references available in the full text version of this article.

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