Local times for two-parameter Lévy processes

Maria E. Vares

Stochastic Processes and their Applications, 1983, vol. 15, issue 1, 59-82

Abstract: In this article we study the problem of existence of jointly continuous local time for two-parameter Lévy processes. Here, 'local time' is understood in the sense of occupation density, kand by 2-parameter Lévy process we mean a process X = {Xz: z [epsilon] [0, +[infinity])2} with independent and stationary increments (over rectangles of the type (s, s'] x (t, t']). We prove that if X is -valued and its lower index is greater than one, then a jointly continuous (at least outside {(x,s,t): x = 0}) local time can be obtained via Berman's method. Also, we extend to 2-parameter processes a result of Getoor and Kesten for usual Lévy processes. Implications in terms of 'approximate local growth' of X are stated.

Date: 1983
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