Numerical evaluation of Wiener integrals

Authors:
Alan G. Konheim and Willard L. Miranker

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

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Abstract: A systematic study of quadrature formulae for the Wiener integral of the type 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.

**[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****[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****[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**, https://doi.org/10.1063/1.1703636**[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****[6]**B. L. van der Waerden,*Moderne Algebra*, Vol. I, Springer, Berlin, 1937; English transl., Ungar, New York, 1949-1950. MR**10**, 587.

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DOI:
https://doi.org/10.1090/S0025-5718-1967-0221753-0

Article copyright:
© Copyright 1967
American Mathematical Society