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Monte-Carlo simulation of stochastic differential systems - a geometrical approach. (English) Zbl 1141.60042
From the authors’ summary: 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 of A. B. Cruzeiro, P. Malliavin and A. Thalmaier [C. R., Math., Acad. Sci. Paris 338, No. 6, 481–486 (2004; Zbl 1046.65006)].

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
Full Text: DOI
[1] Bally, V.; Talay, D., The law of the Euler scheme for stochastic differential equations — I. convergence rate of the distribution function, Probab. theory related fields, 104, 43-60, (1996) · Zbl 0838.60051
[2] Cruzeiro, A.B.; Malliavin, P.; Thalmaier, A., Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation, C. R. acad. sci. Paris, ser. I, 338, 481-486, (2004) · Zbl 1046.65006
[3] Ikeda, N.; Watanabe, S., ()
[4] Kloeden, P.E.; Platen, E., Numerical solution of stochastic differential equations, (1996), Springer-Verlag Berlin · Zbl 0701.60054
[5] Krylov, N.V., ()
[6] Malliavin, P.; Thalmaier, A., Numerical error for SDE: asymptotic expansion and hyperdistributions, C. R. acad. sci. Paris, ser. I, 336, 851-856, (2003) · Zbl 1028.60054
[7] Milstein, G.N., Numerical integration of stochastic differential equations, (1995), Kluwer Acad. Publishers
[8] Stroock, D.W.; Varadhan, S.R.S., ()
[9] Talay, D., Simulation of stochastic differential systems, (), 63-106
[10] Talay, D., ()
[11] Talay, D.; Tubaro, L., Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic anal. appl., 8, 483-509, (1990) · Zbl 0718.60058
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