The ascending ladder height distribution for a certain class of dependent random walks

S. Asmussen and V. Schmidt

Statistica Neerlandica, 1993, vol. 47, issue 4, 269-277

Abstract: A random walk {Sn} with Sn= (Xl ‐ Yl) +…+ (Xn ‐ Yn) is considered where the Xn Yn are non‐negative random variables, the Yn are exponentially distributed with rate δ and the Xn have common distribution function B. It is shown that the expression δ(1 ‐ S (x)) for the density of the ascending ladder height distribution of (Sn), which is well‐known for i.i.d. Xn, holds also when the Xn form a stationary sequence of not necessarily independent random variables.

Date: 1993
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