A note about conditional Ornstein-Uhlenbeck processes

2008/01/21 by Amel Bentata, Bentata, Amel
Economics, Econometrics and Finance · Physics and Astronomy · #60G15 #60J60 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.0801.3261

openalex publication_date 2008/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, the identity in law, which was obtained by P. Salminen, between on one hand, the Ornstein-Uhlenbeck process with parameter gamma, killed when it reaches 0, and on the other hand, the 3-dimensional radial Ornstein-Uhlenbeck process killed exponentially at rate gamma and conditioned to hit 0, is derived from a simple absolute continuity relationship.

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