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1 results

  • The Gillis–Domb–Fisher correlated random walk

  • Anyue Chen, Eric Renshaw
  • Journal:
    Journal of Applied Probability / Volume 29 / Issue 4 / December 1992
    Published online by Cambridge University Press:
    14 July 2016, pp. 792-813
    Print publication:
    December 1992

  • Correlated random walk models figure prominently in many scientific disciplines. Of fundamental importance in such applications is the development of the characteristic function of the n-step probability distribution since it contains complete information on the probability structure of the process. Using a simple algebraic lemma we derive the n-step characteristic function of the Gillis correlated random walk together with other related results. In particular, we present a new and simple proof of Gillis's conjecture, consider the generalization to the Gillis–Domb–Fisher walk, and examine the effect of including an arbitrary initial distribution.