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Monte-Carlo Simulation of Stochastic Differential Systems - a Geometrical Approach

Alves, Carlos J. S.; Cruzeiro, A. B.

Stochastic Processes and Their Applications, 118(3) (2008), 346-367

We develop some numerical schemes for d-dimensional stochastic differential equations derived from Milstein approximations of diffusions which are obtained by lifting the solutions of the stochastic differential equations to higher dimensional spaces using geometrical tools, in the line of the work [A.B. Cruzeiro, P. Malliavin, A. Thalmaier, Geometrization of Monte-Carlo numerical analysis of an elliptic operator: Strong approximation, C. R. Acad. Sci. Paris, Ser. 1338 (2004) 481-486]. (C) 2007 Elsevier B.V. All rights reserved.