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Moments of ladder heights in random walks

  • R. A. Doney (a1)

A well-known result in the theory of random walks states that E{X 2} is finite if and only if E{Z+ } and E{Z_} are both finite (Z + and Z_ being the ladder heights and X a typical step-length) in which case E{X 2} = 2E{Z+ }E{Z_}. This paper contains results relating the existence of moments of X of order ß to the existence of the moments of Z + and Z_ of order ß – 1. The main result is that if β > 2 E{|X|β} < ∞ if and only if and are both finite.

Corresponding author
Postal address: Statistical Laboratory, Department of Mathematics, The University, Manchester M13 9PL, U.K.
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Veraverbere, N. (1977) Asymptotic behaviour of Wiener–Hopf factors of a random walk. Stoch. Proc. Appl. 5, 2737.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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