Stochastic Taylor Expansions: Weight Functions of B-Series Expressed as Multiple Integrals

DOI10.1080/07362990903546504zbMath1188.65005OpenAlexW2049562781MaRDI QIDQ5305281

Kristian Debrabant, Anne Kværnø

Publication date: 19 March 2010

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990903546504

zbMATH Keywords

stochastic differential equationsB-seriesmultiple stochastic integralsstochastic Taylor expansionsWagner-Platen series

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

General order conditions for stochastic partitioned Runge-Kutta methods ⋮ Composition of stochastic B-series with applications to implicit Taylor methods ⋮ B-series analysis of iterated Taylor methods ⋮ Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise

Cites Work

• Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations
• General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
• 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
• Relations between multiple ito and stratonovich integrals
• B–Series Analysis of Stochastic Runge–Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values
• High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations