Abstract
We introduce a class of distribution-valued stochastic processes that arise in the study of pulse reflection from random media and we analyze their asymptotic properties when they are scaled in a natural way.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
Author information
Authors and Affiliations
Additional information
This research was supported by the National Science Foundation under Grants DMS-8201895 and DMS-90003227.
Rights and permissions
About this article
Cite this article
Papanicolaou, G., Weinryb, S. A functional limit theorem for waves reflected by a random medium. Appl Math Optim 30, 307–334 (1994). https://doi.org/10.1007/BF01183015
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01183015