50 citations · 137 across the 16 of their papers we have counts for
18 papers
Direct Inversion for Chi-Square Sampling, the Squared Bessel Process, and Applications
Simon J. A. Malham, Anke Wiese, Yifan Xu
In this paper we derive a new direct inversion method to simulate squared Bessel processes. Since the transition probability of these processes can be represented by a non-central…
The Exponential Lie Series and a Chen-Strichartz Formula for Levy Processes
Kurusch Ebrahimi-Fard, Frederic Patras, Anke Wiese
In this paper, we derive a Chen-Strichartz formula for stochastic differential equations driven by Levy processes, that is, we derive a series expansion of the logarithm of the flo…
Applications of Grassmannian flows to coagulation systems
Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis +1
We demonstrate how many classes of Smoluchowski-type coagulation models can be realised as multiplicative Grassmannian flows and are therefore linearisable, and thus integrable in…
Series expansions and direct inversion for the Heston model
Simon J. A. Malham, Jiaqi Shen, Anke Wiese
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact dis…
Time evolution in quantum systems and stochastics
Anastasia Doikou, Simon J. A. Malham, Anke Wiese
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral…
Applications of Grassmannian flows to integrable systems
Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis +1
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable in the sense that they are realisable as Fredholm Grassmannian flow…
Stochastic analysis & discrete quantum systems
Anastasia Doikou, Simon J. A. Malham, Anke Wiese
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the…
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…
Algebraic structure of stochastic expansions and efficient simulation
Kurusch Ebrahimi-Fard, Alexander Lundervold, Simon J. A. Malham +2
We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators.…
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…
An introduction to SDE simulation
Simon J. A. Malham, Anke Wiese
We outline the basic ideas and techniques underpinning the simulation of stochastic differential equations. In particular we focus on strong simulation and its context. We also pro…
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…
Chi-square simulation of the CIR process and the Heston model
Simon J. A. Malham, Anke Wiese
The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square de…
Efficient strong integrators for linear stochastic systems
Gabriel Lord, Simon J. A. Malham, Anke Wiese
We present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of Wiener processes. These schemes are based on the N…
Stochastic Lie group integrators
Simon J. A. Malham, Anke Wiese
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold.…