Absolute Continuity under Time Shift for Ornstein-Uhlenbeck type Processes with Delay or Anticipation

2014/11/27 by Jörg-Uwe Löbus, Löbus, Jörg-Uwe
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H10 #msc:60J65 #primary 60J65 #secondary 60H10

paper · pdf · doi:10.48550/arxiv.1411.7688

arxiv created 2014/11/27 · arxiv updated 2014/12/01

Abstract

The paper is concerned with one-dimensional two-sided Ornstein-Uhlenbeck type processes with delay or anticipation. We prove existence and uniqueness requiring almost sure boundedness on the left half-axis in case of delay and almost sure boundedness on the right half-axis in case of anticipation. For those stochastic processes (X,P_μ) we calculate the Radon-Nikodym density under time shift of trajectories, P_μ(dX_{⋅ -t})/P_μ(dX), t∈ \Bbb R.

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