Split-step forward methods for stochastic differential equations

Journal of Computational and Applied Mathematics

Volumn 233, Issue 10, 2010, Pages 2641-2651

  Wang, Peng ^a   Li, Yong ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

Euler Maruyama method; Milstein method; Split step method; Stability; Stochastic differential equations

Indexed keywords

ANALYSIS OF STABILITY; EULER-MARUYAMA METHOD; EXPLICIT METHOD; MEAN SQUARE STABILITY; MILSTEIN METHOD; NUMERICAL RESULTS; SPLIT-STEP; SPLIT-STEP METHOD; STOCHASTIC DIFFERENTIAL EQUATIONS; STRONG CONVERGENCE;

DIFFERENTIAL EQUATIONS; MEASUREMENT THEORY; NUMERICAL ANALYSIS; NUMERICAL METHODS; STABILITY; STOCHASTIC SYSTEMS;

EULER EQUATIONS;

EID: 73449111886     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.11.010     Document Type: Article

References (22)

1. Bally V., and Talay D. The law of the Euler scheme for stochastic differential equations I. Convergence rate of the distribution fuction. Probab. Theory Related Fields 104 (1996) 43-60
2. Higham D.J. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43 (2001) 525-546
3. Higham D.J., Mao X., and Stuart A.M. Exponential mean-square stability of numerical solutions to stochastic differential equations. LMS J. Comput. Math. 6 (2003) 297-313
4. Higham D.J., Mao X., and Stuart A.M. Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM J. Numer. Anal. 40 (2002) 1041-1063
5. Kloeden P.E., and Platen E. Higher-order implicit strong numerical schemes for stochastic differential equations. J. Stat. Phys. 66 (1992) 283-314
6. Platen E. An introduction to numerical methods for stochastic differential equations. Acta Numer. 8 (1999) 197-246
7. Kloeden P.E., and Platen E. Numerical Solution of Stochastic Differential Equations (1992), Springer-Verlag, Berlin
8. Maruyama G. Continuous Markov processes and stochastic equations. Rend. Circ. Mat. Palermo 4 (1955) 48-90
9. Milstein G.N. Approximate integration of stochastic differential equations. Theory Probab. Appl. 19 (1974) 557-562
10. Milstein G.N. Numerical Integration of Stochastic Differential Equations (1995), Kluwer, Dordrecht
11. Burrage K., and Tian T.H. The composite Euler method for solving stiff stochastic differential equations. J. Comput. Appl. Math. 131 (2001) 407-426
12. Higham D.J. Mean-square and asymptotic stability of the stochastic theta method. SIAM J. Numer. Anal. 38 (2000) 753-769
13. Tian T.H., and Burrage K. Implicit Taylor methods for stiff stochastic differential equations. Appl. Numer. Math. 38 (2001) 167-185
14. Wang P. Three-stage stochastic Runge-Kutta methods for stochastic differential equations. J. Comput. Appl. Math. 222 (2008) 324-332
15. Wang P., and Liu Z. Split-step backward balanced Milstein methods for stiff stochastic systems. Appl. Numer. Math. 59 (2009) 1198-1213
16. Wang P., Lü X., and Liu Z. Two-stage Milstein methods for stochastic differential equations. Northeast. Math. J. 24 (2008) 63-76
17. Petersen W.P. A general implicit splitting for stabilizing numerical simulations of Itô stochastic differential equations. SIAM. J. Numer. Anal. 35 (1998) 1439-1451
18. Milstein G.N., Platen E., and Schurz H. Balanced implicit methods for stiff stochastic systems. SIAM J. Numer. Anal. 35 (1998) 1010-1019
19. Saito Y., and Mitsui T. Stability analysis of numerical schemes for stochastic differential equations. SIAM J. Numer. Anal. 33 (1996) 2254-2267
20. Burrage K., and Tian T.H. Implicit stochastic Runge-Kutta methods for stochastic differential equations. BIT 44 (2004) 21-39
21. Burrage K., and Tian T.H. Stiffly Accurate Runge-Kutta Methods for stiff stochastic differential equations. Comput. Phys. Comm. 142 (2001) 186-190
22. Hairer E., Lubich C., and Wanner G. Geometric Numerical Integration. first ed. (2002), Springer-Verlag