Jose Blanchet. Xinyun Chen. Jing Dong. “ε-Strong simulation for multidimensional stochastic differential equations via rough path analysis.” Ann. Appl. Probab. 27 (1) 275 – 336, February 2017. https://doi.org/10.1214/16-AAP1204

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Abstract

Consider a multidimensional diffusion process . Let be a deterministic, user defined, tolerance error parameter. Under standard regularity conditions on the drift and diffusion coefficients of , we construct a probability space, supporting both and an explicit, piecewise constant, fully simulatable process such that

with probability one. Moreover, the user can adaptively choose so that (also piecewise constant and fully simulatable) can be constructed conditional on to ensure an error smaller than with probability one. Our construction requires a detailed study of continuity estimates of the Itô map using Lyons’ theory of rough paths. We approximate the underlying Brownian motion, jointly with the Lévy areas with a deterministic error in the underlying rough path metric.

Authors
Jose Blanchet, Xinyun Chen, Jing Dong
Publication date
2017/2/1
Volume
27
Issue
1
Pages
275-336