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Stochastic Lie Group Integrators

Lie group integrators for nonlinear stochastic differential equations with noncommutative vector fields whose solution evolves on a smooth finite-dimensional manifold are presented and some Castell-Gaines methods are uniformly more accurate than the corresponding Stochastic Taylor schemes.
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Algebraic structure of stochastic expansions and efficient simulation

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems. Our motivation is to construct efficient integrators. These are…
Royal Society (opens in a new tab)

Efficient Strong Integrators for Linear Stochastic Systems

It is proved that numerical methods based on the Magnus expansion are more accurate in the mean-square sense than corresponding stochastic Taylor integration schemes.
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An introduction to SDE simulation

The basic ideas and techniques underpinning the simulation of stochastic differential equations and its context are outlined, and the FAQs are addressed.
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Positive and implicit stochastic volatility simulation

For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are…

Stochastic expansions and Hopf algebras

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 the Castell–Gaines…
Royal Society (opens in a new tab)

Chi-square simulation of the CIR process and the Heston model

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 density based on sums…
arXiv (opens in a new tab)

1 81 0 . 08 09 5 v 1 [ m at hph ] 1 8 O ct 2 01 8 Stochastic analysis & discrete quantum systems

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…

N A ] 1 6 O ct 2 00 7 STOCHASTIC LIE GROUP INTEGRATORS

We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group…

Applications of Grassmannian flows to coagulation equations

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 this sense. First,…
arXiv (opens in a new tab)
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