Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical evaluation of Wiener integrals


Authors: Alan G. Konheim and Willard L. Miranker
Journal: Math. Comp. 21 (1967), 49-65
MSC: Primary 65.55
MathSciNet review: 0221753
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A systematic study of quadrature formulae for the Wiener integral $ \int {F[x]w(dx)} $ of the type $ \int {F[\theta (u, \cdot )]\nu (du)} $ is presented. The Cameron and Vladimirov quadrature formulae, which are the function space analogues of Simpson's Rule, are shown to fit into this framework. Numerical results are included.


References [Enhancements On Off] (What's this?)

  • [1] R. H. Cameron, A “Simpson’s rule” for the numerical evaluation of Wiener’s integrals in function space, Duke Math. J. 18 (1951), 111–130. MR 0040589 (12,718d)
  • [2] I. M. Gel′fand, A. S. Frolov, and N. N. Čencov, The computation of continuous integrals by the Monte Carlo method, Izv. Vysš. Učebn. Zaved. Matematika 1958 (1958), no. 5 (6), 32–45 (Russian). MR 0135694 (24 #B1739)
  • [3] I. M. Gel′fand and A. M. Jaglom, Integration in functional spaces and its applications in quantum physics, J. Mathematical Phys. 1 (1960), 48–69. MR 0112604 (22 #3455)
  • [4] R. E. A. C. Paley & N. Wiener, "Fourier transforms in the complex plane," Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc., Providence, R. I., 1934.
  • [5] V. S. Vladimirov, The approximate evaluation of Wiener integrals, Uspehi Mat. Nauk 15 (1960), no. 4 (94), 129–135 (Russian). MR 0124087 (23 #A1404)
  • [6] B. L. van der Waerden, Moderne Algebra, Vol. I, Springer, Berlin, 1937; English transl., Ungar, New York, 1949-1950. MR 10, 587.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.55

Retrieve articles in all journals with MSC: 65.55


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1967-0221753-0
PII: S 0025-5718(1967)0221753-0
Article copyright: © Copyright 1967 American Mathematical Society