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Title: Total variation distance between SDE driven by stable processes and their Euler scheme Authors:  Arnaud Gloter - Universite d Evry Val d Essonne (France) [presenting]
Emmanuelle Clement - Universite Gustave Eiffel (France)
Abstract: The focus is on the rate of convergence to zero for the total variation distance between a class of stochastic differential equations and their Euler scheme. We consider $(X_{i/n})_{i=0,\dots,n}$, a discrete sampling of $X$ solution of a stochastic differential equation driven by a pure jump Lvy process of alpha-Stable type, and $(\hat{X}_{i/n})_{i=0,\dots,n}$, the associated Euler scheme. We give an upper bound for the T.V. distance between the laws of $(X_{i/n})_{i=0,\dots,n}$ and $(\hat{X}_{i/n})_{i=0,\dots,n}$ as $n \to \infty$.