Multi-scaled diffusion-approximation. Applications to wave propagation in random media

Josselin Garnier

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 183-206
  • ISSN: 1292-8100

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Garnier, Josselin. "Multi-scaled diffusion-approximation. Applications to wave propagation in random media." ESAIM: Probability and Statistics 1 (1997): 183-206. <http://eudml.org/doc/104231>.

@article{Garnier1997,
author = {Garnier, Josselin},
journal = {ESAIM: Probability and Statistics},
language = {eng},
pages = {183-206},
publisher = {EDP Sciences},
title = {Multi-scaled diffusion-approximation. Applications to wave propagation in random media},
url = {http://eudml.org/doc/104231},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Garnier, Josselin
TI - Multi-scaled diffusion-approximation. Applications to wave propagation in random media
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 183
EP - 206
LA - eng
UR - http://eudml.org/doc/104231
ER -

References

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  1. ABRAMOWITZ, M. and STEGUN, I. ( 1965). Handbook of mathematical functions, Dover Publications, New-York. 
  2. ALDOUS, D. ( 1978). Stopping times and tightness. Ann. Prob. 6 335-340. Zbl0391.60007MR474446
  3. BAILLY, F. ( 1996) Ph-D thesis. Paris-Sud. 
  4. 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. Zbl0574.60066MR769278
  5. CARMONA, R. ( 1985). Therandom Schrödinger equation, in: Ecole d'été de Probabilités de Saint-Flour, Hennequin, P. L., ed. Lecture Notes in Mathematics, Springer. 
  6. CARMONA, R. and LACROIX, J. ( 1990). Spectral theory of random Schrödinger operators. Birkhauser. Zbl0717.60074MR1102675
  7. COLLINS, R. E. ( 1960). Field theory of guided waves. Mac Graw-Hill, New York. MR116872
  8. 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. Zbl0628.60086MR845723
  9. FARIS, W. G. and TSAY, W. J. ( 1994). Time delay in random scattering. SIAM J. Appl. Math. 54 443-455. Zbl0794.34074MR1265236
  10. GARNIER, J. ( 1996) Ph-D thesis. Ecole Polytechnique. 
  11. GROELL J. E. ( 1968). A circular harmonic computer analysis for rectangular dielectric waveguides. Bell. Syst. Tech. J. 48. 
  12. JAUCH, J., SINHA, K. and MlSRA, B. ( 1972). Time delay in scattering processes. Helv. Phys. Acta 45 398-426. MR418734
  13. KESTEN, J. B. and PAPANICOLAOU, G. ( 1979). A limit theorem for turbulent diffusion. Comm. Math. Phys. 65 97-128. Zbl0399.60049MR528186
  14. 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. 
  15. KNAPP, R., PAPANICOLAOU, G. and WHITE, B. ( 1991). Transmission of waves by a nonlinear random medium. J. of Stat. Phys. 63 567-583. MR1115804
  16. KUSHNER, H. J. ( 1984). Approximation and weak convergence methods for random processes. MIT Press. Zbl0551.60056MR741469
  17. 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. Zbl0549.60041
  18. 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. Zbl0667.73004MR983374
  19. 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). Zbl0387.60067MR461684

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