Numerical evaluation of Wiener integrals
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- by Alan G. Konheim and Willard L. Miranker PDF
- Math. Comp. 21 (1967), 49-65 Request permission
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
- 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 40589
- 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
- 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 112604, DOI 10.1063/1.1703636 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.
- V. S. Vladimirov, The approximate evaluation of Wiener integrals, Uspehi Mat. Nauk 15 (1960), no. 4 (94), 129–135 (Russian). MR 0124087 B. L. van der Waerden, Moderne Algebra, Vol. I, Springer, Berlin, 1937; English transl., Ungar, New York, 1949–1950. MR 10, 587.
Additional Information
- © Copyright 1967 American Mathematical Society
- Journal: Math. Comp. 21 (1967), 49-65
- MSC: Primary 65.55
- DOI: https://doi.org/10.1090/S0025-5718-1967-0221753-0
- MathSciNet review: 0221753