Multi-scaled diffusion-approximation. Applications to wave propagation in random media
ESAIM: Probability and Statistics, Tome 1 (1997), pp. 183-206 
@article{PS_1997__1__183_0,
     author = {Garnier, Josselin},
     title = {Multi-scaled diffusion-approximation. {Applications} to wave propagation in random media},
     journal = {ESAIM: Probability and Statistics},
     pages = {183--206},
     year = {1997},
     publisher = {EDP Sciences},
     volume = {1},
     mrnumber = {1447334},
     zbl = {0930.60061},
     language = {en},
     url = {https://www.numdam.org/item/PS_1997__1__183_0/}
}
TY  - JOUR
AU  - Garnier, Josselin
TI  - Multi-scaled diffusion-approximation. Applications to wave propagation in random media
JO  - ESAIM: Probability and Statistics
PY  - 1997
SP  - 183
EP  - 206
VL  - 1
PB  - EDP Sciences
UR  - https://www.numdam.org/item/PS_1997__1__183_0/
LA  - en
ID  - PS_1997__1__183_0
ER  - 
%0 Journal Article
%A Garnier, Josselin
%T Multi-scaled diffusion-approximation. Applications to wave propagation in random media
%J ESAIM: Probability and Statistics
%D 1997
%P 183-206
%V 1
%I EDP Sciences
%U https://www.numdam.org/item/PS_1997__1__183_0/
%G en
%F PS_1997__1__183_0
Garnier, Josselin. Multi-scaled diffusion-approximation. Applications to wave propagation in random media. ESAIM: Probability and Statistics, Tome 1 (1997), pp. 183-206. https://www.numdam.org/item/PS_1997__1__183_0/

Abramowitz, M. and Stegun, I. ( 1965). Handbook of mathematical functions, Dover Publications, New-York.

Aldous, D. ( 1978). Stopping times and tightness. Ann. Prob. 6 335-340. | Zbl | MR

Bailly, F. ( 1996) Ph-D thesis. Paris-Sud.

Bouc, R. and Pardoux, E. ( 1984). Asymptotic analysis of P.D.E.'s with wide-band noise disturbances and expansions of the moments. Stochastic analysis and Appl. 2 369-422. | Zbl | MR

Carmona, R. ( 1985). Therandom Schrödinger equation, in: Ecole d'été de Probabilités de Saint-Flour, Hennequin, P. L., ed. Lecture Notes in Mathematics, Springer.

Carmona, R. and Lacroix, J. ( 1990). Spectral theory of random Schrödinger operators. Birkhauser. | Zbl | MR

Collins, R. E. ( 1960). Field theory of guided waves. Mac Graw-Hill, New York. | MR

Desvillard, P. and Souillard, B. ( 1986). Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium. J. of Stat. Phys. 43 423-439. | Zbl | MR

Faris, W. G. and Tsay, W. J. ( 1994). Time delay in random scattering. SIAM J. Appl. Math. 54 443-455. | Zbl | MR

Garnier, J. ( 1996) Ph-D thesis. Ecole Polytechnique.

Groell J. E. ( 1968). A circular harmonic computer analysis for rectangular dielectric waveguides. Bell. Syst. Tech. J. 48.

Jauch, J., Sinha, K. and Mlsra, B. ( 1972). Time delay in scattering processes. Helv. Phys. Acta 45 398-426. | MR

Kesten, J. B. and Papanicolaou, G. ( 1979). A limit theorem for turbulent diffusion. Comm. Math. Phys. 65 97-128. | Zbl | MR

Knapp, R., Papanicolaou, G. and White, B. ( 1989). Nonlinearity and localization in one-dimensional random media, in: Disorder and Nonlinearity Bishop, A. R., Campbell, I. K. and Pnevmatikos, S., eds. Springer.

Knapp, R., Papanicolaou, G. and White, B. ( 1991). Transmission of waves by a nonlinear random medium. J. of Stat. Phys. 63 567-583. | MR

Kushner, H. J. ( 1984). Approximation and weak convergence methods for random processes. MIT Press. | Zbl | MR

Metivier M. ( 1984). Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev. Rapport interne CMAP-Ecole Polytechnique. 106.

Papanicolaou, G. ( 1988). Waves in one-dimensional random media, in: Ecole d'été de Probabilités de Saint-Flour, Hennequin, P. L., ed. Lecture Notes in Mathematics, Springer. | Zbl | MR

Papanicolaou, G., Stroock, D. and Varadhan, S. R. S. ( 1976). Martingale approach to some limit theorems, in: Statistical Mechanics andDynamical Systems Ruelle, D., ed. Duke Turbulence Conf. (Duke Univ. Math. Series III, Part VI). | Zbl | MR