An application of the method of moments to stochastic equations
Author:
John J. McCoy
Journal:
Quart. Appl. Math. 26 (1969), 521-536
MSC:
Primary 60.75
DOI:
https://doi.org/10.1090/qam/235629
MathSciNet review:
235629
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Abstract: A modified form of Galerkin’s method is formally applied to an equation involving a stochastic bounded linear operator. The result, in general, is a sequence of stochastic linear algebraic equations. In the case of a statistically homogeneous operator, however, it is possible to obtain a sequence of deterministic linear algebraic equations. The formalism is applied to determining the electric field in a dielectric with a statistically homogeneous random permittivity.
B. G. Galerkin, Vestnik Inzhenerov 1, 897 (1915)
M. V. Keldyš, Izv. Akad. Nauk SSSR Ser. Mat. 6, 309, (1942) (Russian)
L. V. Kantorovič, Uspehi Mat. Nauk. 3 No. 6. 89. (1948) (Russian)
S. G. Mihlin, Direct methods in mathematical physics, GITTL, Moscow, 1948 (Russian)
N. I. Polśkiľ, Dokl. Akad. Nauk SSSR 86, 469 (1952) (Russian)
M. A. Krasnoselśkiľ, Topological methods in the theory of non-linear integral equations, GITTL, Moscow, 1956 (Russian)
- Yu. V. Vorobyev, Method of moments in applied mathematics, Gordon and Breach Science Publishers, New York-London-Paris, 1965. Translated from the Russian by Bernard Seckler. MR 0184400
- Stephen Prager, Diffusion in inhomogeneous media, J. Chem. Phys. 33 (1960), 122–127. MR 112311, DOI https://doi.org/10.1063/1.1731066
W. F. Brown, J. Chem. Phys. 23, 1514 (1955)
- M. Beran and J. Molyneux, Statistical properties of the electric field in a medium with small random variations in permittivity, Nuovo Cimento (10) 30 (1963), 1406–1422 (English, with Italian summary). MR 164422
M. Beran, Nuovo Cimento (10) 38, 777 (1965)
B. G. Galerkin, Vestnik Inzhenerov 1, 897 (1915)
M. V. Keldyš, Izv. Akad. Nauk SSSR Ser. Mat. 6, 309, (1942) (Russian)
L. V. Kantorovič, Uspehi Mat. Nauk. 3 No. 6. 89. (1948) (Russian)
S. G. Mihlin, Direct methods in mathematical physics, GITTL, Moscow, 1948 (Russian)
N. I. Polśkiľ, Dokl. Akad. Nauk SSSR 86, 469 (1952) (Russian)
M. A. Krasnoselśkiľ, Topological methods in the theory of non-linear integral equations, GITTL, Moscow, 1956 (Russian)
Ju. V. Vorobev, Method of moments in applied mathematics, translated from the Russian by B. Seckler, Gordon & Breach, New York, 1965
S. Prager, J. Chem. Phys. 33, 122 (1960)
W. F. Brown, J. Chem. Phys. 23, 1514 (1955)
M. Beran and J. Molyneux, Nuovo Cimento (10) 30, 1406 (1963)
M. Beran, Nuovo Cimento (10) 38, 777 (1965)
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Article copyright:
© Copyright 1969
American Mathematical Society
