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- W2963553212 abstract "In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with $N$ steps is smaller than $O(N^{-2/3+varepsilon})$ where $varepsilon$ is an arbitrary positive constant. This rate is intermediate between the strong error estimation in $O(N^{-1/2})$ obtained when coupling the stochastic differential equation and the Euler scheme with the same Brownian motion and the weak error estimation $O(N^{-1})$ obtained when comparing the expectations of the same function of the diffusion and of the Euler scheme at the terminal time $T$. We also check that the supremum over $tin[0,T]$ of the Wasserstein distance on the space of probability measures on the real line between the laws of the diffusion at time $t$ and the Euler scheme at time $t$ behaves like $O(sqrt{log(N)}N^{-1})$." @default.
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- W2963553212 date "2014-01-01" @default.
- W2963553212 modified "2023-10-15" @default.
- W2963553212 title "Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme" @default.
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