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

Abstract

Consider a multidimensional diffusion process X={X(t):t[0,1]}. Let ε>0 be a deterministic, user defined, tolerance error parameter. Under standard regularity conditions on the drift and diffusion coefficients of X, we construct a probability space, supporting both X and an explicit, piecewise constant, fully simulatable process Xε such that

sup0t1Xε(t)X(t)<ε with probability one. Moreover, the user can adaptively choose ε(0,ε) so that Xε (also piecewise constant and fully simulatable) can be constructed conditional on Xε to ensure an error smaller than ε 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 ε error in the underlying rough path metric.

Citation

Download Citation

Jose Blanchet. Xinyun Chen. Jing Dong. "-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

Information

Received: 1 March 2014; Revised: 1 January 2016; Published: February 2017
First available in Project Euclid: 6 March 2017

zbMATH: 06711461
MathSciNet: MR3619789
Digital Object Identifier: 10.1214/16-AAP1204

Subjects:
Primary: 34K50 , 65C05 , 82B80
Secondary: 97K60

Keywords: Brownian motion , Lévy area , Monte Carlo method , rough path , Stochastic differential equation

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 1 • February 2017
Back to Top