Author:B. V. Budaev Translated by:S. Kislyakov Original publication:
Algebra i Analiz, tom 22 (2010), nomer 6.
St. Petersburg Math. J. 22 (2011), 877-881
August 18, 2011
MathSciNet review:2798765 Full-text PDF
Abstract: The possibility is discussed to improve the ray approximation up to an exact representation of a wave field by the Feynman-Kac probabilistic formula (this formula gives an exact solution of the Helmholtz equation in the form of the expectation of a certain functional on the space of Brownian random walks). Some examples illustrate an application of the solutions obtained to diffraction problems.
V. M. Babich and V. S. Buldyrev, Asymptotic methods in diffraction problems of short-length waves. The method of canonical problems, Nauka, Moscow, 1972; English transl., Short-wavelength diffraction theory. Asymptotic methods, Springer Series on Wave Phenomena, vol. 4, Springer-Verlag, Berlin, 1991. MR 0426630 (54:14569); MR 1245488 (94f:78004)