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

DOI10.1016/j.apnum.2010.11.014zbMath1208.65014arXiv1003.4397OpenAlexW2023863612MaRDI QIDQ623272

Anne Kværnø, Kristian Debrabant

Publication date: 14 February 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4397

zbMATH Keywords

stochastic differential equationnumerical exampleweak approximationorder conditionsstrong approximationrooted treesstochastic B-seriesstochastic Taylor method

Mathematics Subject Classification ID

Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (5)

Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds ⋮ High order numerical integrators for single integrand Stratonovich SDEs ⋮ B-series analysis of iterated Taylor methods ⋮ Stochastic Runge-Kutta Rosenbrock type methods for SDE systems ⋮ Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs

Cites Work

• Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations
• Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge-Kutta family
• A survey of numerical methods for stochastic differential equations
• General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
• Implicit stochastic Runge-Kutta methods for stochastic differential equations
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• Stochastic Taylor Expansions for the Expectation of Functionals of Diffusion Processes
• Stratonovich and Ito Stochastic Taylor Expansions
• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Stochastic Taylor Expansions: Weight Functions of B-Series Expressed as Multiple Integrals
• B–Series Analysis of Stochastic Runge–Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values
• Geometric Numerical Integration
• Coefficients for the study of Runge-Kutta integration processes
• Implicit Taylor methods for stiff stochastic differential equations
• High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

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