Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations

Applied Numerical Mathematics

Volumn 59, Issue 3-4, 2009, Pages 582-594

  Debrabant, Kristian ^a   Rößler, Andreas ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Classification; Optimal scheme; Stochastic differential equation; Stochastic Runge Kutta method; Weak approximation

Indexed keywords

DIFFERENTIAL EQUATIONS; DISPERSIONS; FUNCTION EVALUATION; MEASUREMENT THEORY; NUMBER THEORY; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIAL APPROXIMATION; STOCHASTIC CONTROL SYSTEMS;

CLASSIFICATION; OPTIMAL SCHEME; STOCHASTIC DIFFERENTIAL EQUATION; STOCHASTIC RUNGE-KUTTA METHOD; WEAK APPROXIMATION;

RUNGE KUTTA METHODS;

EID: 58249084804     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.03.012     Document Type: Article

References (13)

1. Burrage K., and Burrage P.M. High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Appl. Numer. Math. 22 1-3 (1996) 81-101
2. Butcher J.C. Numerical Methods for Ordinary Differential Equations (2003), John Wiley & Sons, West Sussex
3. Debrabant K., and Rößler A. Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations. Math. Comput. Simul. 77 4 (2008) 408-420
4. Kloeden P.E., and Platen E. Numerical Solution of Stochastic Differential Equations. Applications of Mathematics vol. 23 (1999), Springer-Verlag, Berlin
5. Komori Y. Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations. J. Comput. Appl. Math. 206 1 (2007) 158-173
6. Mackevicius V., and Navikas J. Second order weak Runge-Kutta type methods for Itô equations. Math. Comput. Simul. 57 1-2 (2001) 29-34
7. Milstein G.N. Numerical Integration of Stochastic Differential Equations (1995), Kluwer Academic Publishers, Dordrecht
8. Rößler A. Rooted tree analysis for order conditions of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations. Stochastic Anal. Appl. 24 1 (2006) 97-134
9. Rößler A. Runge-Kutta methods for Itô stochastic differential equations with scalar noise. BIT 46 1 (2006) 97-110
10. A. Rößler, Second order Runge-Kutta methods for Itô stochastic differential equations, Preprint No. 2479, Technische Universität Darmstadt, 2006
11. Rößler A. Second order Runge-Kutta methods for Stratonovich stochastic differential equations. BIT 47 3 (2007) 657-680
12. Talay D., and Tubaro L. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 4 (1990) 94-120
13. Tocino A., and Vigo-Aguiar J. Weak second order conditions for stochastic Runge-Kutta methods. SIAM J. Sci. Comput. 24 2 (2002) 507-523