The optimal uniform approximation of systems of stochastic differential equations

Annals of Applied Probability

Volumn 12, Issue 2, 2002, Pages 664-690

  Müller Gronbach, Thomas ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Adaptive method; Asymptotic optimality; Pathwise uniform approximation; Systems of stochastic differential equations

Indexed keywords

EID: 0041969994     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1026915620     Document Type: Article

References (14)

1. BOULEAU, N. and LÉPINGLE, D. (1994). Numerical Methods for Stochastic Processes. Wiley, New York.
2. FAURE, O. (1992). Simulation du mouvement brownien et des diffusions. Thèse, ENPC, Paris.
3. HOFMANN, N., MÜLLER-GRONBACH, T. and RITTER, K. (2000a). Optimal approximation of stochastic differential equations by adaptive step-size control. Math. Comp. 69 1017-1034.
4. HOFMANN, N., MÜLLER-GRONBACH, T. and RITTER, K. (2000b). Step-size control for the uniform approximation of systems of stochastic differential equations with additive noise. Ann. Appl. Probab. 10 616-633.
5. HOFMANN, N., MÜLLER-GRONBACH, T. and RITTER, K. (2000c). The optimal discretization of stochastic differential equations. J. Complexity 17 117-153.
6. KARATZAS, I. and SHREVE, S. E. (1999). Methods of Mathematical Finance. Springer, Berlin.
7. KLOEDEN, P. and PLATEN, E. (1995). Numerical Solution of Stochastic Differential Equations. Springer, Berlin.
8. ∞-norm with respect to r-fold Wiener measure. J. Approx. Theory 84 31-40.
9. MILSTEIN, G. N. (1995). Numerical Integration of Stochastic Differential Equations. Kluwer, Dordrecht.
10. MÜLLER-GRONBACH, T. and RITTER, K. (1997). Uniform reconstruction of Gaussian processes. Stochastic Processes Appl. 69 55-70.
11. MÜLLER-GRONBACH, T. and RITTER, K. (1998). Spatial adaption for predicting random functions. Ann. Statist. 26 2264-2288.
12. RITTER, K. (1990). Approximation and optimization on the Wiener space. J. Complexity 6 337-364.
13. TALAY, D. (1995). Simulation of stochastic differential systems. Probabilistic Methods in Applied Physics. Lecture Notes in Phys. 451 54-96. Springer, Berlin.
14. TRAUB, J. F., WASILKOWSKI, G. W. and WOŹNIAKOWSKI, H. (1988). Information-Based Complexity. Academic Press, New York.