SEARCH

SEARCH BY CITATION

References

  • Arnold, V. I. (1989), Mathematical Methods in Classical Mechanics, Grad. Texts Math., vol. 60, 2nd ed., Springer, New York.
  • Budaev, B. V., and D. B. Bogy (2001), Probabilistic solutions of the Helmholtz equations, J. Acoust. Soc. Am., 109(5), 22602262.
  • Budaev, B. V., and D. B. Bogy (2002a), Analysis of one-dimensional wave scattering by the random walk method, J. Acoust. Soc. Am., 111(6), 25552560.
  • Budaev, B. V., and D. B. Bogy (2002b), Application of random walk methods to wave propagation, Q. J. Mech. Appl. Math., 55(2), 209226.
  • Budaev, B. V., and D. B. Bogy (2003), Random walk approach to wave propagation in wedges and cones, J. Acoust. Soc. Am., 114(4), 17331741.
  • Budaev, B. V., and D. B. Bogy (2004), Diffraction by a plane sector, Proc. R. Soc. London, Ser. A, 460(2052), 35293546.
  • Budaev, B. V., and D. B. Bogy (2005a), Diffraction of a plane wave by a sector with Dirichlet or Neumann boundary conditions, IEEE Trans. Antennas Propag., 53(2), 711718.
  • Budaev, B. V., and D. B. Bogy (2005b), Two dimensional diffraction by a wedge with impedance boundary conditions, IEEE Trans. Antennas Propag., 53(6), 20732080.
  • Buslaev, V. S. (1967), Continuun integrals and the asymptotic behavor of the solutions of parabolc equations as t [RIGHTWARDS ARROW] 0: Applications to diffraction, in Topics in Mathematical Physics, edited by S. Berman, pp. 6786, Consult. Bur., New York.
  • Courant, R., K. Friedrichs, and K. H. Lewy (1928), Uber die partiellen Differenzengleichungen der mathematischen Physik, Math. Annal., 100, 3274.
  • Dynkin, E. B. (1965), Markov Processes, Grundlehren Math Wiss. Einzeldarstellungen, vol. 121–122, Springer, New York.
  • Feynman, R. P. (1942), The principle of least action in quantum mechanics, Ph.D. thesis, Princeton Univ., Princeton, N. J.
  • Feynman, R. P. (1948), Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys., 20, 367387.
  • Feynman, R. P. (1998), Statistical Mechanics: A Set of Lectures, Addison-Wesley, Boston, Mass.
  • Fock, V. A. (1965), Electromagnetic Diffraction and Propagation Problems, Int. Ser. Monogr. Electromagn. Waves, vol. 1, Elsevier, New York.
  • Fock, V. A., and M. A. Leontovich (1946), Solution of the problems of propagation of electromagnetic waves along the Earth's surface by the method of parabolic equation, J. Phys. Moscow, 10, 113.
  • Freidlin, M. (1985), Functional Integration and Partial Differential Equations, Annals Math. Stud., vol. 109, Princeton Univ. Press, Princeton, N. J.
  • Galdi, V., L. B. Felsen, and I. M. Pinto (2000), Path integrals for electromagnetics: Are they useful? paper presented at XIII Italian National Conference on Electromagnetics, Ital. Soc. Electromagn., Como, Italy.
  • Ito, K., and H. P. McKean Jr. (1965), Diffusion Processes and Their Sample Paths, Springer, New York.
  • Kac, M. (1949), On distribution of certain Wiener functionals, Trans. Am. Math. Soc., 65(1), 113.
  • Keller, J. B. (1958), A geometric theory of diffraction, in Calculus of Variations and Its Applications, Symp. Appl. Math., vol. 8, pp. 2752, McGraw-Hill, New York.
  • Keller, J. B., and D. W. McLaughlin (1975), The Feynman integral, Am. Math. Mon., 82(5), 451465.
  • Maslov, V. P., and M. V. Fedoriuk (1981), Semi-Classical Approximation in Quantum Mechanics, Springer, New York.
  • Nevels, R. D., J. A. Miller, and R. E. Miller (2000), A path integral time-domain method for electromagnetic scattering, IEEE Trans. Antennas Propag., 48(4), 565573.
  • Osipov, A. V. (2004), A hybrid technique for the analysis of scattering by impedance wedges, paper presented at 2004 International Symposium on Electromagnetic Theory, Union Radio Sci. Int., Pisa, Italy.
  • Petrovsky, I. G. (1934), Über das Irrahrtproblem, Math. Annal., 109, 425444.
  • Philips, H. P., and N. Wiener (1923), Nets and Dirichlet problem, J. Math. Phys., 2, 105124.
  • Schlottmann, R. B. (1999), A path intergal formulation of acoustic wave propagation, Geophys. J. Int., 137(2), 353363.
  • Skorokhod, A. V. (1961), Stochastic equations for diffusion processes in a bounded domain, Theor. Probab. Appl., 6, 264274.
  • Watanabe, S. (1971), On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions, J. Math. Kyoto Univ., 11(1), 169180.
  • Wiener, N. (1923), Differential space, J. Math. Phys., 2, 131174.