A functional limit theorem for waves reflected by a random medium

Applied Mathematics & Optimization - Tập 30 Số 3 - Trang 307-334 - 1994
George Papanicolaou1, Sophie Weinryb2
1Department of Mathematics, Stanford University, Stanford, USA
2Laboratoire de Mathematiques et d'Informatique, Universite Rene Descartes Paris 5, 45 rue des Saints-Peres, 75006, Paris, France

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Asch M., Kohler W., Papanicolaou G., Postel M., White B., Frequency content of randomly scattered signals, SIAM Rev., vol. 33, 1991, pp. 519?625.

Asch M, Papanicolaou G., Postel M., Sheng P., White B., Frequency content of randomly scattered signals. Part I, Wave Motion, vol. 12, 1990, pp. 429?450.

Blankenship G., Papanicolaou G. C., Stability and control of systems with wide-band noise disturbances, I, SIAM J. Appl. Math., vol. 34, 1978, pp. 437?476.

Burridge R., Papanicolaou G., Sheng P., White B., Probing a random medium with a pulse, SIAM J. Appl. Math., vol. 49, 1989, pp. 582?607.

Daubechies I., Orthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., vol. 41, 1988, pp. 909?996.

Fouque J. P., La convergence en loi pour les processus à valeurs dans en espace nucléaire, Ann. Inst. H. Poincaré, vol. 20, 1984, pp. 225?245.

Gihman I. I., Skorohod A. V., Stochastic Differential Equations, Springer-Verlag, New York, 1971.

Kesten H., Papanicolaou G., A limit theorem for turbulent diffusion, Comm. Math. Phys., vol. 65, 1979, pp. 97?128.

Kohler W., Papanicolaou G., Power statistics for wave propagation in one dimension and comparison with transport theory, J. Math. Phys., vol. 14, 1973, pp. 1733?1745, vol. 15, 1974, pp. 2186?2197.

Kohler W., Papanicolaou G., White B., Reflection of waves generated by a point source over a randomly layered medium, Wave Motion, vol. 13, 1991, pp. 53?87.

Kushner H. J., Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory, MIT Press, Cambridge, MA, 1984.

Mitoma I., On sample continuity ofL' processes, J. Math. Soc Japan, vol. 35, 1983.

Papanicolaou G., Asymptotic Analysis of Stochastic Equations, MAA Studies in Mathematics, vol. 18, M. Rosenblatt, ed., Mathematical Association of America, Washington, DC, 1978.

Papanicolaou G. C., Kohler W., Asymptotic theory of mixing stochastic ordinary differential equations, Comm. Pure Appl. Math., vol. XXVII, 1974, pp. 641?688.

Papanicolaou G., Postel M., Sheng P., White B., Frequency content of randomly scattered signals. Part II: Inversion, Wave Motion, vol. 12, 1990, pp. 527?549.

Stroock D. W., Varadhan S. R. S., Multidimensional Diffusion Processes, Springer-Verlag, New York, 1978.