2006/12/22 by Paavo Salminen, Salminen, Paavo, Pierre Vallois +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60J60 #60J65 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J60 #msc:60J65
paper · pdf · doi:10.48550/arxiv.math/0612687
arxiv created 2006/12/22 · openalex publication_date 2006/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting the parameter of the exponential time tend to zero it is seen that these results connect to the corresponding results for excursions of stationary diffusions (in stationary state). We characterize also the laws of the diffusion prior and posterior to the last zero before the exponential time. It is proved using Krein's representations that, e.g., the law of the length of the excursion straddling an exponential time is infinitely divisible. As an illustration of the results we discuss Ornstein-Uhlenbeck processes.