Hellinger and total variation distance in approximating Lévy driven SDEs

2021/03/17 by Emmanuelle Clément, Clément, Emmanuelle
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2103.09648

openalex publication_date 2021/03/17 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28

Abstract

In this paper, we get some convergence rates in total variation distance in approximating discretized paths of Lévy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.

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