### Abstract

Language | English |
---|---|

Article number | 20180567 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 475 |

Issue number | 2221 |

DOIs | |

State | Published - 23 Jan 2019 |

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### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*475*(2221), [20180567]. DOI: 10.1098/rspa.2018.0567

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 475, no. 2221, 20180567. DOI: 10.1098/rspa.2018.0567

**Algebraic Structures and Stochastic Differential Equations driven by Levy processes.** / Curry, Charles; Ebrahimi-Fard, Kurusch; Malham, Simon John A.; Wiese, Anke.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Algebraic Structures and Stochastic Differential Equations driven by Levy processes

AU - Curry,Charles

AU - Ebrahimi-Fard,Kurusch

AU - Malham,Simon John A.

AU - Wiese,Anke

PY - 2019/1/23

Y1 - 2019/1/23

N2 - We construct an efficient integrator for stochastic differential systems driven by Levy 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 Levy processes.

AB - We construct an efficient integrator for stochastic differential systems driven by Levy 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 Levy processes.

U2 - 10.1098/rspa.2018.0567

DO - 10.1098/rspa.2018.0567

M3 - Article

VL - 475

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2221

M1 - 20180567

ER -