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

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  • Rey, Clément

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 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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  • Rey, Clément, 2019. "Approximation of Markov semigroups in total variation distance under an irregular setting: An application to the CIR process," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 539-571.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:2:p:539-571
    DOI: 10.1016/j.spa.2018.03.008
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