Algebraic structures and stochastic differential equations driven by Levy processes
Peer reviewed, Journal article
Published version
Åpne
Permanent lenke
https://hdl.handle.net/11250/2660067Utgivelsesdato
2019Metadata
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- Institutt for matematiske fag [2531]
- Publikasjoner fra CRIStin - NTNU [38518]
Originalversjon
10.1098/rspa.2018.0567Sammendrag
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.