Strong predictor-corrector euler methods for stochastic differential equations

Stochastics and Dynamics

Volumn 8, Issue 3, 2008, Pages 561-581

  Bruti Liberati, Nicola ^a   Platen, Eckhard ^a  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

Asymptotic stability; Simulation methods; Stochastic differential equations; Strong convergence; Strong predictor corrector Euler methods

Indexed keywords

EID: 56549086808     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493708002457     Document Type: Conference Paper

References (25)

1. J. T. Alcock and K. Burrage, A note on the balanced method, BIT Numer. Math. 46 (2006) 689-710.
2. K. Burrage and T. Tian, Predictor-corrector methods of Runge-Kutta type for stochastic differential equations, SIAM J. Numer. Anal. 40 (2002) 1516-1537.
3. P. Glasserman, Monte Carlo Methods in Financial Engineering, Appl. Math., Vol. 53 (Springer, 2004).
4. E. Hairer, S. P. Nørsett and G. Warmer, Solving Ordinary Differential Equations I, Nonstiff Problems (Springer, 1987).
5. D. B. Hernandez and R. Spigler, A-stability of implicit Runge-Kutta methods for systems with additive noise, BIT 32 (1992) 620-633.
6. D. B. Hernandez and R. Spigler, Convergence and stability of implicit Runge-Kutta methods for systems with multiplicative noise, BIT 33 (1993) 654-669.
7. D. Higham and P. Kloeden, Numerical methods for nonlinear stochastic differential equations with jumps, Numer. Math. 110 (2005) 101-119.
8. D. J. Higham, Mean-square and asymptotic stability of numerical methods for stochastic ordinary differential equations, SIAM J. Numer. Anal. 38 (2000) 753-769.
9. N. Hofmann and E. Platen, Stability of weak numerical schemes for stochastic differential equations, Comput. Math. Appl. 28 (1994) 45-57.
10. N. Hofmann and E. Platen, Stability of superimplicit numerical methods for stochastic differential equations, Fields Inst. Commun. 9 (1996) 93-104.
11. P. Jäckel, Monte Carlo Methods in Finance (Wiley, 2002).
12. J. R. Klauder and W. P. Petersen, Numerical integration of multiplicative-noise stochastic differential equations, SIAM J. Numer. Anal. 6 (1985) 1153-1166.
13. P. E. Kloeden and E. Platen, Higher order implicit strong numerical schemes for stochastic differential equations, J. Statist. Phys. 66 (1992) 283-314.
14. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Appl. Math., Vol. 23 (Springer, 1999).
15. P. E. Kloeden, E. Platen and H. Schurz, Numerical Solution of SDE's Through Computer Experiments (Springer, 2003).
16. G. N. Milstein, A theorem of the order of convergence of mean square approximations of systems of stochastic differential equations, Th. Probab. Appl. 32 (1988) 738-741.
17. G. N. Milstein, Numerical Integration of Stochastic Differential Equations (Kluwer, 1995).
18. G. N. Milstein, E. Platen and H. Schurz, Balanced implicit methods for stiff stochastic systems, SIAM J. Numer. Anal. 35 (1998) 1010-1019.
19. E. Platen, On weak implicit and predictor-corrector methods, Math. Comput. Simul. 38 (1995) 69-76.
20. E. Platen and D. Heath, A Benchmark Approach to Quantitative Finance (Springer, 2006).
21. P. Protter, Stochastic Integration and Differential Equations, 2nd edn. (Springer, 2004).
22. Y. Saito and T. Mitsui, Simulation of stochastic differential equations, Ann. Inst. Statist. Math. 45 (1993) 419-432.
23. Y. Saito and T. Mitsui, T-stability of numerical schemes for stochastic differential equations, World Sci. Ser. Appl. Anal., Vol. 2 (World Scientific, 1993).
24. Y. Saito and T. Mitsui, Stability analysis of numerical schemes for stochastic differential equations, SIAM J. Numer. Anal. 33 (1996) 2254-2267.
25. D. Talay, Convergence for each trajectory of an approximation scheme of SDE, Comput. Rend. Acad. Sci. Paris, Sér. I Math. 295 (1982) 249-252 (in French).