Moderate deviations for diffusions in a random gaussian shear flow drift
Annales de l'I.H.P. Probabilités et statistiques, Volume 40 (2004) no. 3, p. 337-366
@article{AIHPB_2004__40_3_337_0,
     author = {Castell, Fabienne},
     title = {Moderate deviations for diffusions in a random gaussian shear flow drift},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {40},
     number = {3},
     year = {2004},
     pages = {337-366},
     doi = {10.1016/j.anihpb.2003.10.003},
     zbl = {1042.60009},
     mrnumber = {2060457},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2004__40_3_337_0}
}
Castell, Fabienne. Moderate deviations for diffusions in a random gaussian shear flow drift. Annales de l'I.H.P. Probabilités et statistiques, Volume 40 (2004) no. 3, pp. 337-366. doi : 10.1016/j.anihpb.2003.10.003. http://www.numdam.org/item/AIHPB_2004__40_3_337_0/

[1] A. Asselah, F. Castell, Quenched large deviations for diffusions in a random Gaussian shear flow drift, Stochastic Process. Appl. 103 (1) (2003) 1-29. | MR 1947958 | Zbl 1075.60508

[2] A. Asselah, F. Castell, Large deviations for Brownian motion in a random scenery, Probab. Theory Related Fields, in press, DOI:10.1007/s00440-003-0276-0. | MR 2001196 | Zbl 1043.60018

[3] M. Avellaneda, A. Majda, Mathematical models with exact renormalization for turbulent transport, Comm. Math. Phys. 131 (1990) 381-429. | MR 1065678 | Zbl 0703.76042

[4] M. Avellaneda, A. Majda, Mathematical models with exact renormalization for turbulent transport II, Comm. Math. Phys. 146 (1992) 139-204. | MR 1163672 | Zbl 0754.76046

[5] M. Biskup, W. König, Long-time tails in the parabolic Anderson model with bounded potential, Ann. Probab. 29 (2) (2001) 636-682. | MR 1849173 | Zbl 1018.60093

[6] H. Brezis, Analyse fonctionnelle. Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983. | MR 697382 | Zbl 0511.46001

[7] R. Carmona, Transport properties of Gaussian velocity fields, in: Real and Stochastic Analysis. Probab. Stochastics Series, CRC, Boca Raton, FL, 1997, pp. 9-63. | MR 1464221 | Zbl 0897.60051

[8] R. Carmona, L. Xu, Homogenization for time dependent 2-D incompressible Gaussian flows, Ann. Appl. Probab. 7 (1) (1997) 265-279. | MR 1428759 | Zbl 0879.60063

[9] F. Castell, F. Pradeilles, Annealed large deviations for diffusions in a random Gaussian shear flow drift, Stochastic Process. Appl. 94 (2001) 171-197. | MR 1840830 | Zbl 1051.60028

[10] T. Chiyonobu, S. Kusuoka, The large deviation principle for hypermixing processes, Probab. Theory Related Fields 78 (4) (1988) 627-649. | MR 950350 | Zbl 0634.60025

[11] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Applications of Mathematics, vol. 38, Springer, New York, 1998. | MR 1619036 | Zbl 0896.60013

[12] M.D. Donsker, S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I, II, Comm. Pure Appl. Math. 28 (1975) 1-47, Comm. Pure Appl. Math. 28 (1975) 279-301. | MR 386024 | Zbl 0348.60031

[13] M.D. Donsker, S.R.S. Varadhan, Asymptotics for the Wiener sausage, Comm. Pure Appl. Math. 28 (1975) 525-565. | MR 397901 | Zbl 0333.60077

[14] A. Fannjiang, T. Komorowski, A martingale approach to homogenization of unbounded random flows, Ann. Probab. 25 (1997) 1872-1894. | MR 1487440 | Zbl 0902.60028

[15] A. Fannjiang, T. Komorowski, An invariance principle for diffusion in turbulence, Ann. Probab. 27 (2) (1999) 751-781. | MR 1698963 | Zbl 0943.60030

[16] A. Fannjiang, T. Komorowski, Turbulent diffusion in Markovian flows, Ann. Appl. Probab. 9 (3) (1999) 591-610. | MR 1722274 | Zbl 0960.60034

[17] A. Fannjiang, T. Komorowski, Fractional Brownian motion limit for a model of turbulent transport, Ann. Appl. Probab. 10 (2000) 1100-1120. | MR 1810866 | Zbl 1073.60532

[18] A. Fannjiang, T. Komorowski, Diffusive and nondiffusive limits of transport in nonmixing flows, SIAM J. Appl. Math. 62 (3) (2002) 909-923. | MR 1897728 | Zbl 0995.60036

[19] A. Fannjiang, G. Papanicolaou, Diffusion in turbulence, Probab. Theory Related Fields 105 (3) (1996) 279-334. | MR 1425865 | Zbl 0847.60062

[20] J. Gärtner, W. König, Moment asymptotics for the continuous parabolic Anderson model, Ann. Appl. Probab. 10 (1) (2000) 192-217. | MR 1765208 | Zbl 01500280

[21] J. Gärtner, W. König, S.A. Molchanov, Almost sure asymptotics for the continuous parabolic Anderson model, Probab. Theory Related Fields 118 (4) (2000) 547-573. | MR 1808375 | Zbl 0972.60056

[22] J. Gärtner, S.A. Molchanov, Parabolic problems for the Anderson model I. Intermittency and related topics, Comm. Math. Phys. 132 (1990) 613-655. | MR 1069840 | Zbl 0711.60055

[23] J. Gärtner, S.A. Molchanov, Parabolic problems for the Anderson model II. Second order asymptotics ans structure of high peaks, Probab. Theory Related Fields 111 (1998) 17-55. | MR 1626766 | Zbl 0909.60040

[24] D. Horntrop, A. Majda, Subtle statistical behavior in simple models for random advection-diffusion, J. Math. Sci. Univ. Tokyo 1 (1) (1994) 23-70. | MR 1298540 | Zbl 0813.76073

[25] H. Kesten, F. Spitzer, A limit theorem related to a new class of self-similar processes, Z. Wahrsch. Verw. Gebiete 50 (1) (1979) 5-25. | MR 550121 | Zbl 0396.60037

[26] T. Komorowski, S. Olla, On the superdiffusive behavior of passive tracer with a Gaussian drift, J. Statist. Phys. 108 (3-4) (2002) 647-668. | Zbl 01879645

[27] C. Landim, S. Olla, H.T. Yau, Convection-diffusion equation with space-time ergodic random flow, Probab. Theory Related Fields 112 (2) (1998) 203-220. | MR 1653837 | Zbl 0914.60070

[28] G. Matheron, G. De Marsily, Is transport in porous media always diffusive? A counterexample, Water Resources Res. 16 (1980) 901-907.

[29] F. Merkl, M.V. Wüthrich, Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential, Probab. Theory Related Fields 119 (2001) 475-507. | MR 1826404 | Zbl 1037.82022

[30] F. Merkl, M.V. Wüthrich, Annealed survival asymptotics for Brownian motion in a scaled Poissonian potential, Stochastic Process. Appl. 96 (2001) 191-211. | MR 1865355 | Zbl 1062.82022

[31] F. Merkl, M.V. Wüthrich, Infinite volume asymptotics of the ground state energy in a scaled Poissonian potential, Ann. I.H. Poincaré-PR 38 (3) (2002) 253-284. | Numdam | MR 1899454 | Zbl 0996.82036

[32] L. Piterbarg, Short-correlation approximation in models of turbulent diffusion, in: Stochastic Models in Geosystems, Minneapolis, MN, 1994, IMA Vol. Math. Appl., vol. 85, Springer, New York, 1997, pp. 313-352. | MR 1480980 | Zbl 0866.60073

[33] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | MR 290095 | Zbl 0207.13501

[34] A.S. Sznitman, Brownian Motion, Obstacles and Random Media, Springer Monographs in Mathematics, Springer, Berlin, 1998. | MR 1717054 | Zbl 0973.60003

[35] M. Talagrand, Sharper bounds for Gaussians and empirical processes, Ann. Probab. 22 (1) (1994) 28-76. | MR 1258865 | Zbl 0798.60051