Approximation via regularization of the local time of semimartingales and Brownian motion

2007/09/04 by Blandine Bérard Bergery, Bergery, Blandine Berard, Pierre Vallois +1
Economics, Econometrics and Finance · Mathematics · #60G44 #60H05 #60H99 #60J55 #60J60 #60J65 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.0709.0402

openalex publication_date 2007/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Through a regularization procedure, few approximation schemes of the local time of a large class of one dimensional processes are given. We mainly consider the local time of continuous semimartingales and reversible diffusions, and the convergence holds in ucp sense. In the case of standard Brownian motion, we have been able to determine a rate of convergence in L², and a.s. convergence of some of our schemes.

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