Stochastic B-series analysis of iterated Taylor methods

Abstract

For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor method, the choice of the iteration method, the predictor and the number of iterations, for Itô and Stratonovich SDEs, and for weak as well as strong convergence are derived. As special case, also the application of Taylor methods to ODEs is considered. The theory is supported by numerical experiments.

References in corpus (2)

• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Composition of stochastic B-series with applications to implicit Taylor methods

Cited by in corpus (4)

• A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
• Composition of stochastic B-series with applications to implicit Taylor methods
• High order numerical integrators for single integrand Stratonovich SDEs
• B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems