The optimal discretization of stochastic differential equations

Journal of Complexity

Volumn 17, Issue 1, 2001, Pages 117-153

  Hofmann, Norbert ^a   Müller Gronbach, Thomas ^b   Ritter, Klaus ^b  

^a GOETHE UNIVERSITY   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Adaptive discretization; Asymptotic optimality; Complexity; Lower bounds; Pathwise approximation; Stochastic differential equation

Indexed keywords

EID: 0035294723     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.2000.0570     Document Type: Article

References (18)

1. Bouleau N., Lépingle D. Numerical Methods for Stochastic Processes. 1994;Wiley, New York.
2. Cambanis S., Hu Y. Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design. Stochastics Stochastics Rep. 59:1996;211-240.
3. Clark J. M. C., Cameron R. J. The maximum rate of convergence of discrete approximations. Grigelionis B. Stochastic Differential Systems. Lecture Notes Control Inf. Sci. 25:1980;162-171 Springer-Verlag, Berlin.
4. Faure O. Simulation du mouvement brownien et des diffusions. 1992;ENPC, Paris.
5. Gaines J. G., Lyons T. J. Variable step size control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math. 57:1997;1455-1484.
6. P. Hertling, Nonlinear Lebesgue and Ito integration problems of high complexity, J. Complexity, in press.
7. Hofmann N., Müller-Gronbach T., Ritter K. Optimal approximation of stochastic differential equations by adaptive step-size control. Math. Comp. 69:2000;1017-1034.
8. N. Hofmann, T. Müller-Gronbach, and K. Ritter, Step-size control for the uniform approximation of systems of stochastic differential equations with additive noise, Ann. Appl. Probab.10, 616-633.
9. Karatzas I., Shreve S. E. Brownian Motion and Stochastic Calculus. 1997;Springer-Verlag, Berlin.
10. Kloeden P., Platen E. Numerical Solution of Stochastic Differential Equations. 1995;Springer-Verlag, Berlin.
11. Mauthner S. Step size control in the numerical solution of stochastic differential equations. J. Comput. Appl. Math. 100:1998;93-109.
12. Milstein G. N. Numerical Integration of Stochastic Differential Equations. 1995;Kluwer Academic, Dordrecht.
13. Newton N. J. An efficient approximation for stochastic differential equations on the partition of symmetrical first passage times. Stochastics Stochastics Rep. 29:1990;227-258.
14. Ritter K. Average-Case Analysis of Numerical Problems. Lecture Notes in Mathematics. 1733:2000;Springer-Verlag, Berlin.
15. Su Y., Cambanis S. Sampling designs for estimation of a random process. Stochastic Processes Appl. 46:1993;47-89.
16. Talay D. Simulation of stochastic differential systems. Krée P., Wedig W. Probabilistic Methods in Applied Physics. Lecture Notes in Physics. 451:1995;54-96 Springer-Verlag, Berlin.
17. Traub J. F., Wasilkowski G. W., Woźniakowski H. Information-Based Complexity. 1988;Academic Press, New York.
18. G. W. Wasilkowski, and, H. Woźniakowski, On the complexity of stochastic integration, Math. Comp, in press.