Quadrature formulas for the wiener measure

Journal of Complexity

Volumn 15, Issue 4, 1999, Pages 476-498

  Steinbauer, Achim ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042885047     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1999.0518     Document Type: Article

References (18)

1. Caflisch R. E., Morokoff W. J., Owen A. B. Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance. 1:1997;27-46.
2. Cameron R. H. A "Simpson's Rule" for the numerical evaluation of Wiener integrals in function space. Duke Math. J. 18:1951;111-130.
3. Chorin A. J. Accurate evaluation of Wiener's integral. Math. Comp. 27:1973;1-15.
4. Egorov A. D., Sobolevsky P. I., Yanovich L. A. Functional Integrals: Approximate Evaluation and Applications. 1993;Kluwer Academic, Dordrecht.
5. Hald O. H. Approximation of Wiener integrals. J. Comput. Phys. 69:1987;460-470.
6. Hildebrand F. B. Introduction to Numerical Analysis. 1956;McGraw-Hill, New York.
7. Karatzas I., Shreve S. E. Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics. 1988;Springer-Verlag, New York.
8. Linetsky V. The path integral approach to financial modeling and options pricing. Comput. Econ. 11:1998;129-163.
9. Lobanov Y. Y. Deterministic computation of functional integrals. Comput. Phys. Comm. 99:1996;59-72.
10. Morokoff W. J. Generating quasi-random paths for stochastic processes. SIAM Rev. 40:1998;765-788.
11. E. Novak, K. Ritter, R. Schmitt, and, A. Steinbauer, On an interpolatory method for high dimensional integration, J. Comput. Appl. Math, in press.
12. Novak E., Ritter K., Steinbauer A. A multiscale method for the evaluation of Wiener integrals. Chui C. K., Schumaker L. L. Approximation Theory IX, Volume 2: Computational Aspects. 1998;251-258 Vanderbilt Univ. Press, Nashville.
13. L. Plaskota, G. W. Wasilkowski, and, H. Woźniakowski, A new algorithm and worst case complexity for Feynman-Kac path integration, manuscript, 1998.
14. Ritter K. Approximation and optimization on the Wiener space. J. Complexity. 6:1990;337-364.
15. Tezuka S. Financial applications of Monte Carlo and quasi-Monte Carlo methods. Hellekalek P., Larcher G. Random and Quasi-Random Point Sets. Lecture Notes in Statistics. 1998;303-332 Springer-Verlag, New York.
16. Traub J. F., Werschulz A. G. Complexity and Information. 1998;Cambridge Univ. Press, Cambridge.
17. Wasilkowski G. W., Woźniakowski H. Explicit cost bounds of algorithms for multivariate tensor product problems. J. Complexity. 11:1995;1-56.
18. Wasilkowski G. W., Woźniakowski H. On tractability of path integration. J. Math. Phys. 37:1996;2071-2088.