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Curry, Charles; Ebrahimi-Fard, Kurusch; Malham, Simon J. A.; Wiese, Anke

Algebraic structures and stochastic differential equations driven by Lévy processes. (English) Zbl 1425.60055

Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2221, Article ID 20180567, 27 p. (2019).
Summary: We construct an efficient integrator for stochastic differential systems driven by Lévy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders and independent of the governing vector fields. This holds provided the driving processes possess moments of all orders and the vector fields are sufficiently smooth. Moreover, the efficient integrator in question is optimal within a broad class of perturbations for half-integer global root mean-square orders of convergence. We obtain these results using the quasi-shuffle algebra of multiple iterated integrals of independent Lévy processes.

Cited in 5 Documents

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
34F05 Ordinary differential equations and systems with randomness

Keywords:

Lévy processes; efficient integrators; quasi-shuffle algebra
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References:

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