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.
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 23 Jan 2019|
- Efficient integrators
- Lévy processes
- Quasi-shuffle algebra
ASJC Scopus subject areas
- Physics and Astronomy(all)