Rossler A. Runge-Kutta Methods for the Numerical Solution of Stochastic Differential Equations

Fachbereich Mathematik
der Technischen Universitat Darmstadt
Fachbereich Mathematik
der Technischen Universitat Darmstadt
Fachbereich Mathematik
der Technischen Universitat Darmstadt
Fachbereich Mathematik
der Technischen Universitat Darmstadt
Shaker Verlag
Aachen: Shaker Verlag, 2003. — 217 p.Introduction
Preliminaries
Theory of Stochastic Differential Equations
Stochastic Taylor Expansions
Numerical Solution of a SDE
Runge-Kutta Methods for SDE Systems with One Wiener Process
Deterministic Runge-Kutta Methods
Convergence of Weak Schemes
Local and Global Weak Approximations
Rooted Tree Theory
S-Trees
Ita SDE Systems
Stratonovich SDE Systems
Stochastic Runge-Kutta Methods
Expansion of the SRK method
General Order Conditions
Some Explicit Stochastic Runge-Kutta Methods
Stochastic Runge-Kutta Methods for Ita SDE Systems
Stochastic Runge-Kutta Methods for Stratonovich SDE Systems
SDE Systems with a Multi-Dimensional Wiener Process
Extended Rooted Tree Theory
Ita SDE Systems
Stratonovich SDE Systems
Stochastic Runge-Kutta Methods for General SDE Systems
Expansion of the SRK method
General Order Conditions
Some Explicit Stochastic Runge-Kutta Methods
Stochastic Runge-Kutta Methods for Ita SDE Systems
SRK Methods for Stratonovich SD E Systems with Commutative Noise
Simulation Study
Monte Carlo Simulations of SDEs
Numerical Simulation
Conclusion
A Stochastic Rooted Trees
B Proofs for Order Conditions
C Proofs for Order Conditions
List of Figures
List of Tables
Bibliography