Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Lévy processes

Abstract : We consider the Euler approximation of stochastic differential equations (SDEs) driven by Lévy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y=Z(V) with V a subordinator and Z a stable process, we propose an approximation Y by Z(Vn) where Vn is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs.
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Stochastic Processes and their Applications, Elsevier, 2003, 108 (1), pp.Pages 1-26. 〈10.1016/S0304-4149(03)00100-5〉
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https://hal.univ-cotedazur.fr/hal-00755435
Contributeur : Sylvain Rubenthaler <>
Soumis le : mercredi 21 novembre 2012 - 11:38:36
Dernière modification le : jeudi 3 mai 2018 - 13:32:58

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Sylvain Rubenthaler, Magnus Wiktorsson. Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Lévy processes. Stochastic Processes and their Applications, Elsevier, 2003, 108 (1), pp.Pages 1-26. 〈10.1016/S0304-4149(03)00100-5〉. 〈hal-00755435〉

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