Order Conditions of Stochastic Runge--Kutta Methods by B-Series
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 38 (5) , 1626-1646
- https://doi.org/10.1137/s0036142999363206
Abstract
In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theoryKeywords
This publication has 10 references indexed in Scilit:
- High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formulaPhysica D: Nonlinear Phenomena, 1999
- Step size control in the numerical solution of stochastic differential equationsJournal of Computational and Applied Mathematics, 1998
- General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systemsApplied Numerical Mathematics, 1998
- A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equationsBIT Numerical Mathematics, 1997
- Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equationsBIT Numerical Mathematics, 1997
- High strong order explicit Runge-Kutta methods for stochastic ordinary differential equationsApplied Numerical Mathematics, 1996
- Numerical Integration of Stochastic Differential EquationsPublished by Springer Nature ,1995
- Flots et series de Taylor stochastiquesProbability Theory and Related Fields, 1989
- Numerical Treatment of Stochastic Differential EquationsSIAM Journal on Numerical Analysis, 1982
- Continuous Markov processes and stochastic equationsRendiconti del Circolo Matematico di Palermo Series 2, 1955