Independence times for iid sequences, random walks and Lévy processes

2017/04/20 by Matija Vidmar, Vidmar, Matija · 1 citation
Chemistry · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G10 #60G50 #60G51 #Chemistry #Combinatorics #Discrete mathematics #Distribution (mathematics) #FOS: Mathematics #Independence (probability theory) #Lévy process #Mathematical analysis #Mathematics #Physics #Probability (math.PR) #Probability and Risk Models #Random sequence #Random variable #Random walk #Sequence (biology) #Statistical physics #Statistics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G10 #msc:60G50 #msc:60G51

paper · pdf · doi:10.48550/arxiv.1704.06198

published in arXiv (Cornell University) (Cornell University) · 18 pages

openalex publication_date 2017/04/20 · arxiv created 2018/09/28 · arxiv updated 2018/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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