Duals and inverse flows of generalized Ornstein-Uhlenbeck processes

2025/04/07 by Anita Behme, Behme, Anita, Henriette E. Heinrich +3
Mathematics · #60G10 #60G51 #60H10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G10 #msc:60G51 #msc:60H10

paper · pdf · doi:10.48550/arxiv.2504.05157

23 pages

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

We derive explicit representations for the (Siegmund) dual and the inverse flow of generalized Ornstein-Uhlenbeck processes whenever these exist. It turns out that the dual and the process corresponding to the inverse stochastic flow are again generalized Ornstein-Uhlenbeck processes. Further, we observe that the stationary distribution of the dual process provides information about the hitting time of zero of the original process.

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