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 journalArticle

Abstract

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
Volume475
Issue number2221
DOIs
Publication statusPublished - 23 Jan 2019

Fingerprint

integrators
Algebraic Structure
Stochastic Equations
Differential equations
differential equations
Differential equation
Vector Field
Iterated integral
Algebra
Strong Approximation
Shuffle
Order of Convergence
approximation
Stochastic Systems
Differential System
Mean Square
integers
algebra
Roots
Moment

Keywords

  • Efficient integrators
  • Lévy processes
  • Quasi-shuffle algebra

ASJC Scopus subject areas

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

Cite this

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Algebraic structures and stochastic differential equations driven by Lévy processes. / Curry, Charles; Ebrahimi-Fard, Kurusch; Malham, Simon John A.; Wiese, Anke.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, No. 2221, 20180567, 23.01.2019.

Research output: Contribution to journalArticle

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