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Spitzer's condition for random walks and Lévy Processes by J. Bertoin; R.A. Doney is a Mathematics article available to read on EtoBox.

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Spitzer's condition holds for a random walk 5' if the probabilities pn = P{S, > 0} converge in CCsaro mean to p, and for a Levy process X at co (at 0, respectively) if t-l J,' p(s)& + p as t -+ 00(O), where p(s) = P{X,5 > 0). It has been shown in Doney [4] that if 0 < p <: 1 then this happens for a random walk if and only if plL converges to p. We show here that this result extends to the cases p = 0 and p = 1, and also that Spitzer's condition holds for a Levy process at m(O) if and only if p(t) -+ p as t -+ co(O).

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Author

J. Bertoin; R.A. Doney

Publisher

Elsevier Science; Institute of Mathematical Statistics; Elsevier BV (ISSN 0246-0203)

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)