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Monte-Carlo simulation of stochastic differential systems — a geometrical approach

2007; Elsevier BV; Volume: 118; Issue: 3 Linguagem: Inglês

10.1016/j.spa.2007.04.009

1879-209X

Carlos J.S. Alves, Ana Bela Cruzeiro,

Probabilistic and Robust Engineering Design

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. I 338 (2004) 481–486].