Composition of stochastic B-series with applications to implicit Taylor methods

Abstract

In this article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we apply these order conditions to derive in a simple manner a family of strong order 1.5 Taylor methods applicable to Itô SDEs.

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References in corpus (3)

• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Stochastic Taylor expansions for the expectation of functionals of diffusion processes
• Stochastic B-series analysis of iterated Taylor methods

Cited by in corpus (6)

• Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
• Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs
• Stochastic B-series analysis of iterated Taylor methods
• High order numerical integrators for single integrand Stratonovich SDEs
• Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
• B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems