Trajectorial coupling between one-dimensional diffusions with linear diffusion coefficient and their Euler scheme
نویسندگان
چکیده
It is well known that the strong error approximation, in the space of continuous paths equipped with the supremum norm, between a diffusion process, with smooth coefficients, and its Euler approximation with step $1/n$ is $O(nˆ{-1/2})$ and that the weak error estimation between the marginal laws, at the terminal time $T$, is $O(nˆ{-1})$. In this talk, we study the $p-$Wasserstein distance between the law of the trajectory of a diffusion process, with linear diffusion coefficient, and its Euler scheme. Using the Komlós, Major and Tusnády construction, we show that this Wasserstein distance is of order $log n/n$. ∗Speaker †Corresponding author: [email protected] sciencesconf.org:montecarlo16:114748
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