Algebraic structures and stochastic differential equations driven by Lévy processes

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
246 Downloads (Pure)


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.

Original languageEnglish
Article number20180567
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2221
Publication statusPublished - 23 Jan 2019


  • Efficient integrators
  • Lévy processes
  • Quasi-shuffle algebra

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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