Almost sure weak convergence of the increments of Lévy processes

Mario Wschebor

Stochastic Processes and their Applications, 1995, vol. 55, issue 2, 253-270

Abstract: Let (Xt : t >= 0) be a stochastically continuous, real valued stochastic process with independent homogeneous increments, cadlag paths, X0 = 0. We consider the behaviour, for fixed [omega] as h [downwards arrow] 0, of the increments (Xt + h - Xt)/a(h) as a function of t in [0, 1] with Lebesgue measure, a(·) belonging to some natural class of functions. Generally speaking, it is not possible to find a(·) so that almost surely the normalized increments have a non-trivial limit in Lp([0, 1], [lambda])(0

Keywords: Lévy; process; Increments; Almost; sure; weak; convergence (search for similar items in EconPapers)
Date: 1995
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