, According to this definition we have D 1 ? for t large enough, so we can use the lower bounds for P(A 1 (? ? ? 1 (h t /2)) ? e ht(1+?)/2 ) and P(A 1, )) ? e ht
, Random walks in random environment: What a single trajectory tells, Israel Journal of Mathematics, vol.8, issue.1, pp.205-220, 2004.
DOI : 10.1007/BF02771533
URL : https://hal.archives-ouvertes.fr/hal-00103060
, On the estimation of the potential of Sinai???s RWRE, Brazilian Journal of Probability and Statistics, vol.25, issue.2, pp.121-235, 2011.
DOI : 10.1214/09-BJPS113
, Localization and number of visited valleys for a transient diffusion in random environment, Electronic Journal of Probability, vol.20, issue.0, pp.1-59, 2015.
DOI : 10.1214/EJP.v20-3173
URL : https://hal.archives-ouvertes.fr/hal-00908626
, Renewal structure and local time for diffusions in random environment, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01152982
, Limit Law of the Local Time for Brox???s Diffusion, Journal of Theoretical Probability, vol.28, issue.3, pp.634-656, 2011.
DOI : 10.1007/s10959-010-0314-7
, Dna unzipping via stopped birth and death processes with random probability transition, Appl Math Res Express, vol.2012, pp.184-208, 2012.
DOI : 10.1093/amrx/abs008
URL : http://arxiv.org/abs/1101.0559
, Hidden Markov model for parameter estimation of a random walk in a Markov environment, ESAIM: Probability and Statistics, vol.19, pp.605-625, 2015.
DOI : 10.1051/ps/2015008
URL : https://hal.archives-ouvertes.fr/hal-01025035
, On Continuity Properties of the Law of Integrals of L??vy Processes, pp.137-159, 1934.
DOI : 10.1007/978-3-540-77913-1_6
, On Subordinators, Self-Similar Markov Processes and Some Factorizations of the Exponential Variable, Electronic Communications in Probability, vol.6, issue.0, pp.95-106, 2001.
DOI : 10.1214/ECP.v6-1039
, On the entire moments of self-similar Markov processes and exponential functionals of L??vy processes, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.11, issue.1, pp.33-45, 2002.
DOI : 10.5802/afst.1016
, Exponential functionals of L??vy processes, Probability Surveys, vol.2, issue.0, pp.191-212, 2005.
DOI : 10.1214/154957805100000122
, Convergence of Probability Measures, INC, 1999.
DOI : 10.1002/9780470316962
, Regular Variation, 1987.
DOI : 10.1017/CBO9780511721434
, Handbook of Brownian Motion-Facts and Formulae, Birkhäuser, 1996.
, Extremes, sums, levy processes, and ageing. Lecture, 2010.
, A One-Dimensional Diffusion Process in a Wiener Medium, The Annals of Probability, vol.14, issue.4, pp.1206-1218, 1986.
DOI : 10.1214/aop/1176992363
, The mean velocity of a Brownian motion in a random L??vy
potential, The Annals of Probability, vol.25, issue.4, pp.1774-1788, 1997.
DOI : 10.1214/aop/1023481110
, Sur les fonctionnelles exponentielles de certains processus de l??vy, Stochastics An International Journal of Probability and Stochastic Processes, vol.47, issue.1, pp.71-101, 1994.
DOI : 10.1080/17442509408833883
, On the distribution and asymptotic results for exponential functionals of Lévy processes, Exponential functionals and principal values related to Brownian motion, pp.73-130, 1997.
, One-dimensional diffusion in an asymmetric random environment Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.715-726, 2006.
, Localization of favorite points for diffusion in a random environment, Stochastic Processes and their Applications, pp.1159-1189, 2008.
DOI : 10.1016/j.spa.2007.07.015
, Replication of a multicomponent chain, by the "lightning mechanism, Biophysics, vol.12, pp.336-341, 1967.
, Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support. preprint, arxiv 1404, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00976413
, Maximum likelihood estimator consistency for a ballistic random walk in a parametric random environment. Stochastic Process, 26] A. Dembo, N. Gantert, Y. Peres, and Z. Shi. Valleys and the maximal local time for random walk in random environment. Probability Theory and Related Fields, pp.268-288, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00744629
, The Maximum of the Local Time of a Diffusion Process in a Drifted Brownian Potential, 2006.
DOI : 10.1007/978-3-319-44465-9_5
URL : https://hal.archives-ouvertes.fr/hal-00022214
, The Maximum of the Local Time of a Diffusion Process in a Drifted Brownian Potential, 2016.
DOI : 10.1007/978-3-319-44465-9_5
URL : https://hal.archives-ouvertes.fr/hal-00022214
, Local time of a diffusion in a stable L??vy environment, Stochastics An International Journal of Probability and Stochastic Processes, vol.39, issue.2, pp.127-152, 2011.
DOI : 10.1214/009117906000000539
, Fluctuation Theory for Lévy Processes (Summer school, St-Floor France), 2005.
DOI : 10.1007/978-1-4612-0197-7_3
, Laguerre Series for Asian and Other Options, Mathematical Finance, vol.10, issue.4, pp.407-428, 2000.
DOI : 10.1111/1467-9965.00101
, Path decompositions for real Lévy processes Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.339-370, 2003.
DOI : 10.1016/s0246-0203(02)00004-3
URL : http://arxiv.org/abs/math/0509520
, Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime, Bulletin de la Société mathématique de France, vol.137, issue.3, pp.423-452, 2009.
DOI : 10.24033/bsmf.2580
URL : https://hal.archives-ouvertes.fr/hal-00185933
, Limit laws for transient random walks in random environment on Z. Annales de l'institut Fourier, pp.2469-2508, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00137770
, A probabilistic representation of constants in kesten's renewal theorem. Probability Theory and Related Fields, pp.581-613, 2009.
, The alternating marked point process of h-slopes of drifted Brownian motion, Stochastic Processes and their Applications, vol.119, issue.6, pp.1765-1791, 2009.
DOI : 10.1016/j.spa.2008.09.002
, Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment, Mathematical Methods of Statistics, vol.23, issue.1, pp.1-19, 2014.
DOI : 10.3103/S1066530714010013
URL : https://hal.archives-ouvertes.fr/hal-00783980
, An Introduction to Probability Theory, 1971.
, The infinite valley for a recurrent random walk in random environment, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, pp.525-536, 2010.
DOI : 10.1214/09-AIHP205
URL : https://hal.archives-ouvertes.fr/hal-00485283
, Many visits to a single site by a transient random walk in random environment, Stochastic Processes and their Applications, vol.99, issue.2, pp.159-176, 2002.
DOI : 10.1016/S0304-4149(02)00089-3
, On limiting distribution for a random walk in a critical onedimensional random environment. Com. of the Mosc, Math. Soc, pp.199-200, 1986.
, The problem of the most visited site in random environment, Probability Theory and Related Fields, vol.116, issue.2, pp.273-302, 2000.
DOI : 10.1007/PL00008730
, Rates of convergence of diffusions with drifted brownian potential, Trans. Amer, Math. Soc, issue.10, pp.3513915-3934, 1999.
, A diffusion process in a Brownian environment with drift, J. Math. Soc. Japan, vol.49, pp.189-211, 1997.
DOI : 10.1142/9789812778550_0028
, Invariance principle for a Brownian motion with large drift in a white noise environment, Hiroshima Math. J, vol.28, issue.1, pp.129-137, 1998.
DOI : 10.1142/9789812778550_0030
, The limit distribution of Sinai's random walk in random environment, Physica A: Statistical Mechanics and its Applications, vol.138, issue.1-2, pp.299-309, 1986.
DOI : 10.1016/0378-4371(86)90186-X
, A limit law for random walk in a random environment, Comp. Math, vol.30, pp.145-168, 1975.
, Single molecule statistics and the polynucleotide unzipping transition, Physical Review E, vol.98, issue.3, p.31917, 2002.
DOI : 10.1103/PhysRevE.65.031917
URL : http://arxiv.org/abs/cond-mat/0107423
, Zero White Noise Limit through Dirichlet forms, with application to diffusions in a random medium, Probability Theory and Related Fields, vol.1247, issue.1, pp.549-480, 1994.
DOI : 10.1007/BF01206232
, Limit theorems for diffusions with a random potential, Stochastic Processes and their Applications, vol.60, issue.1, pp.103-111, 1995.
DOI : 10.1016/0304-4149(95)00057-7
URL : http://doi.org/10.1016/0304-4149(95)00057-7
, Tail asymptotics for exponential functionals of L??vy processes, Stochastic Processes and their Applications, pp.156-177, 2006.
DOI : 10.1016/j.spa.2005.09.002
, Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion, Lecture Notes Math. Bernoulli, vol.27, issue.5A, pp.239-247, 1989.
DOI : 10.1137/1127028
, A refined factorization of the exponential law, Bernoulli, vol.17, issue.2, pp.814-826, 2011.
DOI : 10.3150/10-BEJ292
, Point processes, regular variation and weak convergence, Advances in Applied Probability, vol.13, issue.01, pp.66-138, 1986.
DOI : 10.1137/1116067
, Continuous martingales and Brownian motion. Number 293, 1999.
, Recurrent extensions of self-similar Markov processes and Cram??r's condition, Bernoulli, vol.11, issue.3, pp.471-509, 2005.
DOI : 10.3150/bj/1120591185
URL : http://arxiv.org/pdf/0711.4442v1.pdf
, Lévy Processes and Infinitely Divisible Distributions. Cambridge studies in advanced mathematics, 1999.
, Diffusions with random coefficients, Contemp. Math, vol.41, pp.351-356, 1985.
DOI : 10.1090/conm/041/814724
, A local time curiosity in random environment, Stochastic Processes and their Applications, vol.76, issue.2, pp.231-250, 1998.
DOI : 10.1016/S0304-4149(98)00036-2
, Convergence in Skorokhod J-topology for compositions of stochastic processes, Theory Stoch. Process, vol.14, issue.1, pp.126-143, 2008.
, The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium, Theory of Probability & Its Applications, vol.27, issue.2, pp.256-268, 1982.
DOI : 10.1137/1127028
, Limiting behavior of a diffusion in an asymptotically stable environment Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.101-138, 2007.
, A Slow Transient Diffusion in a Drifted Stable Potential, Journal of Theoretical Probability, vol.8, issue.11, pp.153-166, 2007.
DOI : 10.1007/s10959-007-0056-3
URL : https://hal.archives-ouvertes.fr/hal-00157856
, Rates of convergence of a transient diffusion in a spectrally negative L??vy potential, The Annals of Probability, vol.36, issue.1, pp.279-318, 2008.
DOI : 10.1214/009117907000000123
, Annealed tail estimates for a Brownian motion in a drifted Brownian potential, The Annals of Probability, vol.35, issue.1, pp.32-67, 2007.
DOI : 10.1214/009117906000000539
, Recurrence of a diffusion process in a multidimensional Brownian environment, Proceedings of the Japan Academy, Series A, Mathematical Sciences, vol.69, issue.9, pp.377-381, 1993.
DOI : 10.3792/pjaa.69.377
, Limit theorems for a Brownian motion with drift in a white noise environment, Chaos, Solitons & Fractals, vol.8, issue.11, pp.1807-1816, 1997.
DOI : 10.1016/S0960-0779(97)00029-5
, Limit theorems for a Brownian motion with drift in a white noise environment, Chaos, Solitons & Fractals, vol.8, issue.11, pp.1807-1816, 1997.
DOI : 10.1016/S0960-0779(97)00029-5
, One dimensional random walk in two component chain, Soviet Math. Dokl, vol.13, issue.5, 1972.
, Exponential functionals of spectrally one-sided Lévy processes conditioned to stay positive, 1507.
, Almost sure behavior for the local time of a diffusion in a spectrally negative Lévy environment
, Path decompostion of spectrally negative Lévy processes, and application to the local time of a diffusion in those environments, 2016.
, Stochastic-Process Limits : An Introduction to Stochastic-Process Limits and Their Application to Queues, 1989.
, Lectures notes on random walks in random environment. St Flour Summer School, pp.189-312, 2001.