50 citations · 202 across the 30 of their papers we have counts for
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Algebraic Structures and Stochastic Differential Equations driven by Levy processes
Charles Curry, Kurusch Ebrahimi-Fard, Simon J. A. Malham +1
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…
The exponential Lie series for continuous semimartingales
Kurusch Ebrahimi-Fard, Simon J. A. Malham, Frederic Patras +1
We consider stochastic differential systems driven by continuous semimartingales and governed by non-commuting vector fields. We prove that the logarithm of the flowmap is an expon…
Flows and stochastic Taylor series in Ito calculus
Kurusch Ebrahimi-Fard, Simon J. A. Malham, Frederic Patras +1
For stochastic systems driven by continuous semimartingales an explicit formula for the logarithm of the Ito flow map is given. A similar formula is also obtained for solutions of…
Levy Processes and Quasi-Shuffle Algebras
Charles Curry, Kurusch Ebrahimi-Fard, Simon J. A. Malham +1
We investigate the algebra of repeated integrals of semimartingales. We prove that a minimal family of semimartingales generates a quasi-shuffle algebra. In essence, to fulfill the…
Efficient almost-exact Levy area sampling
Simon J. A. Malham, Anke Wiese
We present a new method for sampling the Levy area for a two-dimensional Wiener process conditioned on its endpoints. An efficient sampler for the Levy area is required to implemen…
Stochastic expansions and Hopf algebras
Simon J. A. Malham, Anke Wiese
We study solutions to nonlinear stochastic differential systems driven by a multi-dimensional Wiener process. A useful algorithm for strongly simulating such stochastic systems is…