Independence times for iid sequences, random walks and Lévy processes

Matija Vidmar

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3619-3637

Abstract: For a sequence in discrete time having stationary independent values (respectively, random walk) X, those random times R of X are characterized set-theoretically, for which the strict post-R sequence (respectively, the process of the increments of X after R) is independent of the history up to R. For a Lévy process X and a random time R of X, reasonably useful sufficient conditions and a partial necessary condition on R are given, for the process of the increments of X after R to be independent of the history up to R.

Keywords: Processes with stationary independent values; Processes with stationary independent increments; Independence; Strong Markov property; Path decompositions (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.10.003

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