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• W2229153149 abstract "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(n −1/2) and that the weak error estimation between the marginal laws, at the terminal time T , is O(n −1). An analysis of the weak trajectorial error has been developed by Alfonsi, Jourdain and Kohatsu-Higa [1], through the study of the p−Wasserstein distance between the two processes. For a one-dimensional diffusion, they obtained an intermediate rate for the pathwise Wasserstein distance of order n −2/3+e. Using the Komlos , Major and Tusnady construction, we improve this bound in the case of the geometric Brownian motion and we obtain a rate of order log n/n. MSC 2010. 65C30, 60H35." @default.
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• W2229153149 date "2015-06-24" @default.
• W2229153149 modified "2023-09-26" @default.
• W2229153149 title "An application of the KMT construction to the pathwise weak error in the Euler approximation of the geometric Brownian motion" @default.
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