Approximation of Markov semigroups in total variation distance under an irregular setting: An application to the CIR process

Abstract : In this paper, we propose a method to prove the total variation convergence of approximation of Markov semigroups with singularities. In particular our approach is adapted to the study of numerical schemes for Stochastic Differential Equation (SDE) with simply locally smooth coefficients. First we present this method and then, we apply it to the CIR process. In particular, we consider the weak second order scheme introduced in [2] (Alfonsi 2010) and we prove that it also converges towards the CIR diffusion process for the total variation distance. This convergence occurs with almost order two.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01412024
Contributeur : Clément Rey <>
Soumis le : mercredi 22 novembre 2017 - 15:14:36
Dernière modification le : jeudi 11 janvier 2018 - 06:12:30

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  • HAL Id : hal-01412024, version 3

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INSMI | UPMC | USPC | PMA

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Clément Rey. Approximation of Markov semigroups in total variation distance under an irregular setting: An application to the CIR process. 2017. 〈hal-01412024v3〉

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