Soliton perturbations and the random Kepler problem, Physica D: Nonlinear Phenomena, vol.135, issue.3-4, pp.369-386, 2000. ,
DOI : 10.1016/S0167-2789(99)00118-9
Evolution of randomly modulated solitons in optical fibers, Optics Communications, vol.126, issue.1-3, pp.89-94, 1996. ,
DOI : 10.1016/0030-4018(96)00049-1
Stochastic calculus with respect to Gaussian processes, Ann. Probab, vol.29, pp.766-801, 1999. ,
Stochastic integration with respect to the fractional Brownian motion, Stochastics An International Journal of Probability and Stochastic Processes, vol.75, issue.3, pp.129-152, 2003. ,
DOI : 10.1080/1045112031000078917
Grandes déviations et applications, inÉcolein´inÉcole d'´ eté de Probabilité de Saint-Flour, Lecture Notes in Math, pp.774-775, 1980. ,
Formule de Taylor stochastique et développements asymptotiques d'intégrales de Feynman, Séminaire de probabilités XIV, pp.921-237, 1982. ,
DOI : 10.1007/bfb0092653
Petites perturbations aléatoires des systèmes dynamiques: développements asymptotiques, Bull. Sc. Math, vol.109, pp.253-308 ,
Espaces de Wiener et Fonctions Aléatoires Gaussiennes, Lecture Notes in Math, vol.379, 1974. ,
DOI : 10.1007/bfb0060493
URL : http://dx.doi.org/10.1016/0001-8708(76)90173-0
Two complementary descriptions of intermittency, Physical Review E, vol.57, issue.2, pp.1231-1234, 1998. ,
DOI : 10.1103/PhysRevE.57.R1231
Temperature effects in a nonlinear model of monolayer Scheibe aggregates, Physical Review E, vol.49, issue.5, pp.4627-4636, 1994. ,
DOI : 10.1103/PhysRevE.49.4627
White noise in the two-dimensional nonlinear schr??dinger equation, Applicable Analysis, vol.57, issue.1, pp.3-15, 1995. ,
DOI : 10.1080/00036819508840335
Nonlinear and stochastic modelling of energy transfer in Scheibe aggregates, Math. and Computers in Simulation, vol.40, pp.339-358, 1996. ,
Numerical study of two-dimensional stochastic NLS equations, Numerical Methods for Partial Differential Equations, vol.71, issue.4, pp.810-842, 2005. ,
DOI : 10.1002/num.20064
URL : https://hal.archives-ouvertes.fr/hal-00001470
Méthodes de Laplace et de la phase stationnaire sur l'espace de Wiener, Stochastics Stochastics Rep, vol.25, pp.125-153, 1988. ,
Thermal diffusion of envelope solitons on anharmonic atomic chains, The European Physical Journal B, vol.28, issue.1, pp.103-112, 2004. ,
DOI : 10.1140/epjb/e2004-00361-0
Stochastic partial differential equations in M-type 2 Banach spaces, Potential Analysis, vol.278, issue.3???4, pp.1-45, 1995. ,
DOI : 10.1007/BF01048965
On stochastic convolution in banach spaces and applications, Stochastics and Stochastic Reports, vol.1180, issue.3-4, pp.245-295, 1997. ,
DOI : 10.1016/0022-0396(82)90075-4
Perel'man, On the stability of solitary waves for nonlinear Schrödinger equations, Am. Math. Soc. Transl. Ser, vol.2, pp.74-98, 1995. ,
On asymptotic stability of solitary waves for nonlinear Schr??dinger equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.20, issue.3, pp.419-475, 2003. ,
DOI : 10.1016/S0294-1449(02)00018-5
One-dimensional Variational Problems, Lecture Series in Math. and its Appl, p.15, 1998. ,
Large deviations for Burger's type SPDE, Stochastic Process, Appl, vol.84, pp.53-70, 1999. ,
Interest rate models: from parametric statistics to infinite dimensional stochastic analysis, lecture notes of a course at Princeton university, 2001. ,
Stochastic integration with respect to fractional brownian motion, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.39, issue.1, pp.27-68, 2003. ,
DOI : 10.1016/S0246-0203(02)01111-1
An Introduction to Nonlinear Schrödinger Equations, 1993. ,
Orbital stability of satnding waves of nonlinear Schrödinger equations, Ann. Int. H. Poincaré An. non Lin, vol.85, pp.549-561, 1982. ,
Large deviations for stochastic reaction-diffusion with multiplicative noise and non-lipschitz reaction term, Ann. Probab, vol.32, pp.1100-1139, 2004. ,
Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and nonlipschitz reaction term, Ann. Inst. H. Poincaré Probab. Statist, pp.41-69, 2005. ,
Uniform large deviations for parabolic SPDEs and applications, Stochastic Process, Appl, vol.72, pp.161-187, 1997. ,
The large deviation principle for hypermixing processes, Probab. Theory Relat, pp.627-649, 1988. ,
Stabilization of solutions to nonlinear Schrödinger equations, Comm. Pure Appl. Math, vol.54, pp.110-1145, 2001. ,
On asymptotic stability of ground states of NLS, Rend, Istit. Mat. Univ. Trieste, vol.32, pp.105-118, 2002. ,
Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Relat, pp.108-140, 2002. ,
DOI : 10.1007/s004400100158
Stochastic Equations in Infinite Dimensions, of Mathematics and its Applications, 1992. ,
A random wave process, Applied Mathematics & Optimization, vol.8, issue.1, pp.97-114, 1984. ,
DOI : 10.1007/BF01449037
A Stochastic Nonlinear Schr??dinger Equation??with Multiplicative Noise, Communications in Mathematical Physics, vol.205, issue.1, pp.161-181, 1999. ,
DOI : 10.1007/s002200050672
The Stochastic Nonlinear Schrödinger Equation in H 1 , Stochastic Anal, Appl, vol.21, pp.97-126, 2003. ,
On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation, Probab. Theory Relat, pp.76-96, 2002. ,
Blow-up for the stochastic nonlinear Schr??dinger equation with multiplicative noise, The Annals of Probability, vol.33, issue.3, pp.1078-1110, 2005. ,
DOI : 10.1214/009117904000000964
Finite-time blow-up in the additive supercritical stochastic nonlinear Schr??dinger equation: the real noise case, Contemporary Mathematics, vol.301, pp.183-194, 2002. ,
DOI : 10.1090/conm/301/05164
Stochastic integration with respect to Volterra processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.41, issue.2, pp.123-149, 2005. ,
DOI : 10.1016/j.anihpb.2004.03.004
URL : https://hal.archives-ouvertes.fr/hal-00358143
Stochastic analysis of the fractional Brownian motion, Potential Anal, pp.177-214, 1997. ,
Numerical simulation of focusing stochastic nonlinear Schr??dinger equations, Physica D: Nonlinear Phenomena, vol.162, issue.3-4, pp.131-154, 2002. ,
DOI : 10.1016/S0167-2789(01)00379-7
Small noise asymptotic of the timing jitter in soliton transmission, preprint IRMAR and CREST, 2005. ,
Ergodicity for the weakly damped stochastic non-linear Schrödinger equations ,
Numerical simulation of the stochastic Korteweg???de Vries equation, Physica D: Nonlinear Phenomena, vol.134, issue.2, pp.200-226, 1999. ,
DOI : 10.1016/S0167-2789(99)00072-X
Genealogical particle analysis of rare events, The Annals of Applied Probability, vol.15, issue.4, 2005. ,
DOI : 10.1214/105051605000000566
URL : https://hal.archives-ouvertes.fr/hal-00113982
Non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission, Optics Letters, vol.28, issue.21, pp.2097-2099, 2003. ,
DOI : 10.1364/OL.28.002097
Non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission, Optics Letters, vol.28, issue.21, pp.2097-2099, 2003. ,
DOI : 10.1364/OL.28.002097
Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems, Journal of the Optical Society of America B, vol.22, issue.4, pp.2097-2099, 2003. ,
DOI : 10.1364/JOSAB.22.000743
Erbium-Doped Fiber Amplifiers, 2002. ,
DOI : 10.1201/9780203904657.ch10
Asymptotic evaluation of certain Markov processes for large time, I, Comm. Pure Appl, Math, vol.28, pp.1-47, 1975. ,
Asymptotic evaluation of certain markov process expectations for large time, II, Communications on Pure and Applied Mathematics, vol.28, issue.2, pp.279-301, 1975. ,
DOI : 10.1002/cpa.3160280206
Asymptotic evaluation of certain Markov process expectations for large time???III, Communications on Pure and Applied Mathematics, vol.19, issue.4, pp.389-461, 1976. ,
DOI : 10.1002/cpa.3160290405
Asymptotic evaluation of certain Markov processes for large time, IV, Comm. Pure Appl. Math, pp.36-183, 1983. ,
Asymptotics for the polaron, Communications on Pure and Applied Mathematics, vol.57, issue.4, pp.36-505, 1983. ,
DOI : 10.1002/cpa.3160360408
Quantum noise in optical fibers. II. Raman jitter in soliton communications, J. Opt. Soc. Am. B, vol.18, pp.153-161, 2001. ,
Pasik-Duncan, Fractional Brownian motion and linear stochastic equations in Hilbert space, Stochastic Dyn, pp.225-250, 2002. ,
Partial Differential Equations, Grad. Stud. in Math, vol.119, 1998. ,
Statistics of soliton-bearing systems with additive noise, Physical Review E, vol.63, issue.2, p.25601, 2001. ,
DOI : 10.1103/PhysRevE.63.025601
Non-Gaussian error probability in optical soliton transmission, Physica D: Nonlinear Phenomena, vol.195, issue.1-2, pp.195-196, 2004. ,
DOI : 10.1016/j.physd.2004.01.044
Statistics of interacting optical solitons, Physical Review E, vol.64, issue.6, p.67602, 2001. ,
DOI : 10.1103/PhysRevE.64.067602
Role of interaction in causing errors in optical soliton transmission, Optics Letters, vol.27, issue.1, pp.13-15, 2003. ,
DOI : 10.1364/OL.27.000013
A study of a class of stochastic differential equations with non-Lipschitzian coefficients, Probability Theory and Related Fields, vol.91, issue.3, pp.356-390, 2005. ,
DOI : 10.1007/s00440-004-0398-z
Large fluctuations for a nonlinear heat equation with noise, Journal of Physics A: Mathematical and General, vol.15, issue.10, pp.3025-3055, 1982. ,
DOI : 10.1088/0305-4470/15/10/011
Random Perturbations of Reaction-Diffusion Equations: The Quasi-Deterministic Approximation, Transactions of the American Mathematical Society, vol.305, issue.2, pp.665-697, 1988. ,
DOI : 10.2307/2000884
Random perturbations of nonlinear oscillators, The Annals of Probability, vol.26, issue.3, pp.925-967, 1998. ,
DOI : 10.1214/aop/1022855739
A remark on random perturbations of the nonlinear pendulum, The Annals of Applied Probability, vol.9, issue.3, pp.611-628, 1999. ,
DOI : 10.1214/aoap/1029962806
On random perturbations of Hamiltonian systems with many degrees of freedom, Stochastic Process, Appl, vol.94, pp.199-239, 2001. ,
Random perturbations of dynamical systems and diffusion processes with conservation laws, Probability Theory and Related Fields, vol.128, issue.3, pp.441-466, 2004. ,
DOI : 10.1007/s00440-003-0312-0
Random perturbations of dynamical systems, p.205, 1998. ,
Diffusion Processes on Graphs and the Averaging Principle, The Annals of Probability, vol.21, issue.4, pp.2215-2245, 1993. ,
DOI : 10.1214/aop/1176989018
Solitary Wave Dynamics in an External Potential, Communications in Mathematical Physics, vol.16, issue.3, pp.613-642, 2004. ,
DOI : 10.1007/s00220-004-1128-1
Asymptotic Transmission of Solitons through Random Media, SIAM Journal on Applied Mathematics, vol.58, issue.6, pp.1969-1995, 1998. ,
DOI : 10.1137/S0036139997318573
Solitons in random media with long-range correlation, Waves in Random Media, vol.63, issue.3, pp.149-162, 2001. ,
DOI : 10.1080/13616670109409780
Effective pulse dynamics in optical fibers with polarization mode dispersion, preprint LSP, 2004. ,
EDP stochastiques : approches de type mesure martingale et semi-groupe d'´ evolution autour d'uné equation de la neurophysiologie , mémoire du cours de lecture du DEA modélisation stochastique et statistique d, 2001. ,
Théorèmes de support dans le cas d'une diffusion et de l'´ equation de Burgers stochastique, mémoire du DEA modélisation stochastique et statistique d, 2001. ,
Large deviations and support results for nonlinear Schr??dinger equations with additive noise and applications, ESAIM: Probability and Statistics, vol.9, pp.74-97, 2005. ,
DOI : 10.1051/ps:2005005
Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise, Stochastic Process, Appl, vol.115, pp.1904-1927, 2005. ,
Large deviations for stochastic nonlinear Schrödinger equations and applications, 2005. ,
Exit from a neighborhood of zero for weakly damped stochastic nonlinear Schrödinger equations, preprint IRMAR and CREST, 2005. ,
Study of the non-Gaussian timing jitter statistics induced by soliton interaction and filtering, Optics Communications, vol.123, issue.4-6, pp.617-623, 1996. ,
DOI : 10.1016/0030-4018(95)00599-4
Finite dimensional behavior for weakly damped driven Schr??dinger equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.5, issue.4, pp.365-405, 1988. ,
DOI : 10.1016/S0294-1449(16)30343-2
On the blowing up of solutions to the Cauchy problem for nonlinear Schr??dinger equations, Journal of Mathematical Physics, vol.18, issue.9, pp.1794-1797, 1977. ,
DOI : 10.1063/1.523491
Random walk of coherently amplified solitons in optical fiber transmission, Optics Letters, vol.11, issue.10, pp.665-667, 1986. ,
DOI : 10.1364/OL.11.000665
Dispersive perturbations of solitons of the nonlinear Schr??dinger equation, Journal of the Optical Society of America B, vol.9, issue.1, pp.91-97, 1992. ,
DOI : 10.1364/JOSAB.9.000091
Regularity of the attractor for a weakly damped nonlinear schr??dinger equation, Applicable Analysis, vol.58, issue.1-2, pp.99-119, 1996. ,
DOI : 10.1080/00036819608840420
Stability theory of solitary waves in the presence of symmetry, I, Journal of Functional Analysis, vol.74, issue.1, pp.160-197, 1987. ,
DOI : 10.1016/0022-1236(87)90044-9
Influence of stochasticity on multiple four-wave-mixing processes in an optical fiber, Phys. Rev. E, vol.66, p.66609, 2002. ,
Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion, Applied Physics Letters, vol.23, issue.3, pp.142-144, 1973. ,
DOI : 10.1063/1.1654836
Quantum theory of soliton squeezing: a linearized approach, Journal of the Optical Society of America B, vol.7, issue.3, pp.386-392, 1990. ,
DOI : 10.1364/JOSAB.7.000386
Effective action for stochastic partial differential equations, Physical Review E, vol.60, issue.6, pp.6343-6360, 1999. ,
DOI : 10.1103/PhysRevE.60.6343
URL : http://arxiv.org/abs/cond-mat/9904215
Principles of large deviations for the empirical processes of the Ornsetin-Uhlenbeck process, J. Theoret. Probab, vol.12, pp.61-75, 1999. ,
Non-Gaussian statistics of soliton timing jitter induced by amplifier noise, Optics Letters, vol.28, issue.22, pp.2165-2167, 2003. ,
DOI : 10.1364/OL.28.002165
Raman noise and soliton squeezing, Journal of the Optical Society of America B, vol.11, issue.7, pp.1267-1276, 1994. ,
DOI : 10.1364/JOSAB.11.001267
On Nonlinear Schrödinger Equation, Ann. Inst. H. Poincaré Phys. Théor, vol.46, pp.113-129, 1987. ,
Fluctuational Escape and Related Phenomena in Nonlinear Optical Systems, Modern Nonlinear Optics, Part, vol.3, pp.469-524, 2001. ,
DOI : 10.1002/0471231495.ch8
Influence of stochasticity on multiple four-wave-mixing processes in an optical fiber, Physical Review E, vol.66, issue.6, p.66609, 2002. ,
DOI : 10.1103/PhysRevE.66.066609
Random perturbations of 2-dimensional hamiltonian flows, Probability Theory and Related Fields, vol.129, issue.1, pp.37-62, 2004. ,
DOI : 10.1007/s00440-003-0320-0
L??vy area of Wiener processes in Banach spaces, The Annals of Probability, vol.30, issue.2, pp.546-578, 2002. ,
DOI : 10.1214/aop/1023481002
Large deviations and support theorem for diffusion process via rough paths, Stochastic Process, Appl, vol.102, pp.265-283, 2002. ,
Experiments on Critical Phenomena in a Noisy Exit Problem, Physical Review Letters, vol.79, issue.17, pp.79-3109, 1997. ,
DOI : 10.1103/PhysRevLett.79.3109
Differential equations driven by rough signals, Revista Matem??tica Iberoamericana, vol.14, pp.215-310, 1998. ,
DOI : 10.4171/RMI/240
System Control and Rough Paths, 2000. ,
DOI : 10.1090/fic/034/07
Evolution equations driven by a fractional Brownian motion, Journal of Functional Analysis, vol.202, issue.1, pp.277-305, 2003. ,
DOI : 10.1016/S0022-1236(02)00065-4
Probability-density function for energy perturbations of isolated optical pulses, Optics Express, vol.11, issue.26, pp.3628-3648, 2003. ,
DOI : 10.1364/OE.11.003628
Non-Gaussian corrections to the Gordon???Haus distribution resulting from soliton interactions, Optics Letters, vol.20, issue.3, pp.285-287, 1995. ,
DOI : 10.1364/OL.20.000285
Sanz-Solé, A simple proof of the support theorem for diffusion processes, Lecture Notes in Math, pp.35-48, 1994. ,
Sanz-Solé, Large deviations for rough paths of the fractional Brownian motion, published online in Ann ,
Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems, Optics Letters, vol.28, issue.2, pp.105-107, 2003. ,
DOI : 10.1364/OL.28.000105
Large deviations w.r.t. quasi-every starting point for symmetric right processes on general state spaces, Probab. Theory Related Fields, vol.99, pp.527-548, 1994. ,
Large deviation principle for stochastic evolution equations, Probab. Theory Related Fields 98, pp.113-136, 1994. ,
DOI : 10.1007/bf01311351
Exponential tail estimates for infinite-dimensional stochastic convolutions, Bull. Pol. Acad. Sci, vol.40, pp.323-333, 1992. ,
Aspects théoriques et numériques de l'´ equation de Korteweg-de Vries stochastique, Thèse de l, 1998. ,
Remarques sur les petites perturbations de systemes dynamiques, Séminaire de Probabilités XVI, pp.184-200, 1980. ,
DOI : 10.1070/RM1970v025n01ABEH001254
URL : http://archive.numdam.org/article/SPS_1982__16__184_0.pdf
A LDP result for the strong Arc-Sine law, Journal of Theoretical Probability, vol.15, issue.3, pp.793-815, 2002. ,
DOI : 10.1023/A:1016280117892
Sharp Laplace Asymptotics For a Parabolic SPDE, Stochastics An International Journal of Probability and Stochastic Processes, vol.69, issue.1, pp.11-30, 2000. ,
DOI : 10.1080/17442500008834230
Sharp large deviation estimates for a certain class of sets on the Wiener space, Bulletin des Sciences Math??matiques, vol.124, issue.7, pp.525-555, 2000. ,
DOI : 10.1016/S0007-4497(00)01062-9
Sharp large deviation estimates for the stochastic heat equation, Potential Analysis, vol.14, issue.4, pp.409-435, 2001. ,
DOI : 10.1023/A:1011286304117
Sharp Laplace asymptotics for a hyperbolic SPDE, in Stochastic analysis and related topics VII, pp.225-244, 2001. ,
Thermal vortex dynamics in two-dimensional condensate, Phys. Rev. B, vol.62, pp.1238-1243 ,
Mathematical models for stochastic evolutions, Quartes Jornades d'investigació i foment de la Multidisciplinarietat, pp.1-29, 2002. ,
Instability of nonlinear bound states, Communications in Mathematical Physics, vol.96, issue.2, pp.173-190, 1985. ,
DOI : 10.1007/BF01212446
Optimal control of large fluctuations, Physical Review E, vol.55, issue.3, pp.2516-2521, 1997. ,
DOI : 10.1103/PhysRevE.55.2516
Fluctuations, Escape, and Nucleation in Driven Systems: Logarithmic Susceptibility, Physical Review Letters, vol.79, issue.17, pp.79-3113, 1997. ,
DOI : 10.1103/PhysRevLett.79.3113
Selection of the ground state for nonlinear Schrödinger equations ,
Large Deviations for a Reaction-Diffusion Equation with Non-Gaussian Perturbations, The Annals of Probability, vol.20, issue.1, pp.504-537, 1992. ,
DOI : 10.1214/aop/1176989939
Large deviations for the invariant measure of a reactiondiffusion equation with non-Gaussian perturbations, pp.393-421, 1992. ,
Stochastic averaging with a flattened Hamiltonian: a Markov process on a stratified space (a whiskered sphere, Transactions of the American Mathematical Society, vol.354, issue.03, pp.853-900, 2001. ,
DOI : 10.1090/S0002-9947-01-02903-8
Stochastic Averaging Near a Homoclinic Orbit with Multiplicative Noise, Stochastics and Dynamics, vol.03, issue.03, pp.299-391, 2003. ,
DOI : 10.1142/S0219493703000759
A boundary layer theory for diffusively perturbed transport aroud a heteroclinic cycle, Comm. on Pure and Appl. Math, vol.152, pp.299-391, 2004. ,
The Nonlinear Schrödinger Equation, Self- Focusing and Wave Collapse, Appl. Math. Sciences, 1999. ,
Stochastic evolution equations with fractional Brownian motion, Probab, pp.186-204, 2003. ,
Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schr??dinger Equations, SIAM Journal on Mathematical Analysis, vol.15, issue.2, pp.357-366, 1984. ,
DOI : 10.1137/0515028
An introduction to stochastic partial differential equations , inÉcolein´inÉcole d'´ eté de Probabilité de Saint-Flour, Lecture Notes in Math, pp.1180-265, 1986. ,
Lyapunov stability of ground states of nonlinear dispersive evolution equations, Communications on Pure and Applied Mathematics, vol.38, issue.1, pp.51-68, 1986. ,
DOI : 10.1002/cpa.3160390103
Hizanidis, Motion of 2D Schrödinger solitary waves in the presence of random external potentials, Physica Scripta, pp.65-363, 2002. ,