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Independence times for iid sequences, random walks and Lévy processes

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  • Vidmar, Matija

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.

Suggested Citation

  • Vidmar, Matija, 2019. "Independence times for iid sequences, random walks and Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3619-3637.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3619-3637
    DOI: 10.1016/j.spa.2018.10.003
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