R. Abraham and J. Delmas, Feller Property and Infinitesimal Generator of the Exploration Process, Journal of Theoretical Probability, vol.26, issue.1, pp.355-370, 2007.
DOI : 10.1007/s10959-007-0082-1
URL : https://hal.archives-ouvertes.fr/hal-00015553

R. Abraham and J. Delmas, Williams??? decomposition of the L??vy continuum random tree and simultaneous extinction probability for populations with neutral mutations, Stochastic Processes and their Applications, vol.119, issue.4, pp.1124-1143, 2008.
DOI : 10.1016/j.spa.2008.06.001

R. Abraham and J. Delmas, Changing the branching mechanism of a continuous state branching process using immigration, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.45, issue.1, pp.226-238, 2009.
DOI : 10.1214/07-AIHP165
URL : https://hal.archives-ouvertes.fr/hal-00096275

R. Abraham and J. Delmas, Fragmentation associated with L??vy processes using snake, Probability Theory and Related Fields, vol.131, issue.3, pp.113-154, 2008.
DOI : 10.1007/s00440-007-0081-2

R. Abraham and J. Delmas, A continuum-tree-valued Markov process. prépublication
URL : https://hal.archives-ouvertes.fr/hal-00379118

R. Abraham, J. Delmas, and G. Voisin, Pruning a Lévy continuum random tree. prépublication

R. Abraham and L. Serlet, Poisson Snake and Fragmentation, Electronic Journal of Probability, vol.7, issue.0, 2002.
DOI : 10.1214/EJP.v7-116
URL : https://hal.archives-ouvertes.fr/hal-00170693

D. Aldous and J. Pitman, The standard additive coalescent, Ann. Probab, vol.26, pp.1703-1726, 1998.

P. Andreoletti, Almost sure estimates for the concentration neighborhood of Sinai's walk. Stoch, Proc. App, pp.1473-1490, 2007.

P. Andreoletti and R. Diel, Limit law of the local time for Brox's diffusion. Prépublication

A. Basdevant, Fragmentation of Ordered Partitions and Intervals, Electronic Journal of Probability, vol.11, issue.0, pp.394-417, 2006.
DOI : 10.1214/EJP.v11-323
URL : https://hal.archives-ouvertes.fr/hal-00085444

J. Bertoin, Lévy processes, 1996.

J. Bertoin, Random fragmentation and coagulation processes. Cambridge Studies in Advanced Mathematics, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00103015

J. Bertoin, The asymptotic behavior of fragmentation processes, Journal of the European Mathematical Society, vol.5, issue.4, pp.395-416, 2003.
DOI : 10.1007/s10097-003-0055-3
URL : https://hal.archives-ouvertes.fr/hal-00104740

J. Bertoin, Homogeneous fragmentation processes, Probability Theory and Related Fields, vol.121, issue.3, pp.301-318, 2001.
DOI : 10.1007/s004400100152

J. Bertoin, Self-similar fragmentations, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.38, issue.3, pp.319-340, 2000.
DOI : 10.1016/S0246-0203(00)01073-6
URL : https://hal.archives-ouvertes.fr/hal-00101984

J. Bertoin, A fragmentation process connected to Brownian motion, Probability Theory and Related Fields, vol.117, issue.2, pp.289-301, 2000.
DOI : 10.1007/s004400050008

J. Bertoin, The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. publication
URL : https://hal.archives-ouvertes.fr/hal-00414695

J. Bertoin, Splitting at the infimum and excursions in half-lines for random walks and L??vy processes, Stoch. Proc. App, pp.17-35, 1993.
DOI : 10.1016/0304-4149(93)90092-I

J. Bertoin, Sur la décomposition de la trajectoire d'un processus de Lévy spectrallement positif en son infimum, Ann. Inst. Henri Poincaré, vol.27, pp.537-547, 1991.

J. Bertoin and J. Gall, The Bolthausen-Sznitman coalescent and the genealogy of continuous state branching processes, Probab. Th. Rel. Fields, vol.117, pp.249-266, 2000.

J. Bertoin, J. Gall, Y. Le, and . Jan, Spatial branching processes and subordination. Canad, J. of Math, vol.49, pp.24-54, 1997.

N. H. Bingham, Continuous branching processes and spectral positivity, Stoch. Proc. App, pp.217-242, 1976.
DOI : 10.1016/0304-4149(76)90011-9

R. M. Blumenthal, Excursions of Markov processes, Birkhäuser, 1992.
DOI : 10.1007/978-1-4684-9412-9

P. Buneman, A note on the metric properties of trees, Journal of Combinatorial Theory, Series B, vol.17, issue.1, pp.48-50, 1974.
DOI : 10.1016/0095-8956(74)90047-1

. Th and . Brox, A one-dimensional diffusion process in a Wiener medium, Ann. Probab, vol.14, issue.4, pp.1206-1218, 1986.

P. Carmona, 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

D. J. Daley and D. Vere-jones, An introduction to the theory of point processes, II. Probability and its Applications General theory and structures, 2008.

D. A. Dawson, Measure-valued Markov processes Ecole d'´ eté de Probabilités de Saint-Flour, pp.1-260, 1991.

J. Delmas, Fragmentation at height associated with L??vy processes, Stochastic Processes and their Applications, vol.117, issue.3, pp.297-311, 2007.
DOI : 10.1016/j.spa.2006.06.001

J. Delmas, Height process for super-critical continuous state branching process, Markov Proc. and Rel. Fields, pp.309-326, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00112029

A. Dembo, N. Gantert, Y. Peres, and Z. Shi, Valleys and the Maximum Local Time for Random Walk in Random Environment, Probability Theory and Related Fields, vol.27, issue.3-4, pp.443-473, 2007.
DOI : 10.1007/s00440-006-0005-6
URL : https://hal.archives-ouvertes.fr/hal-00128037

A. Devulder, The Maximum of the Local Time of a Diffusion Process in a Drifted Brownian Potential
DOI : 10.1007/978-3-319-44465-9_5
URL : https://hal.archives-ouvertes.fr/hal-00022214

R. Diel and G. Voisin, Local time of a diffusion in a stable L??vy environment, Stochastics An International Journal of Probability and Stochastic Processes, vol.39, issue.2
DOI : 10.1214/009117906000000539

R. A. Doney, Fluctuation theory for Lévy processes. Ecole d'´ eté de Probabilités de Saint-Flour XXXV, 2005.

R. A. Doney and A. E. Kyprianou, Overshoots and undershoots of L??vy processes, The Annals of Applied Probability, vol.16, issue.1, pp.91-106, 2006.
DOI : 10.1214/105051605000000647

T. Duquesne, Path decompositions for real Levy processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.39, issue.2, pp.339-370, 2003.
DOI : 10.1016/S0246-0203(02)00004-3

T. Duquesne and J. Gall, Random trees, Lévy processes and spatial branching processes, 2002.

T. Duquesne and J. Gall, Probabilistic and fractal aspects of L???vy trees, Probability Theory and Related Fields, vol.101, issue.4, pp.553-603, 2005.
DOI : 10.1007/s00440-004-0385-4

S. N. Evans, Snakes and spiders: Brownian motion on ???-trees, Probability Theory and Related Fields, vol.117, issue.3, pp.361-386, 2000.
DOI : 10.1007/s004400050010

S. N. Evans, Probability and real trees. Ecole d'´ eté de Probabilités de Saint-Flour XXXV, 2005.

S. N. Evans and J. Pitman, Construction of Markovian coalescents, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.34, issue.3, pp.339-383, 1998.
DOI : 10.1016/S0246-0203(98)80015-0

S. N. Evans, J. Pitman, and A. Winter, Rayleigh processes, real trees, and root growth with re-grafting, Probability Theory and Related Fields, vol.18, issue.1, pp.81-126, 2006.
DOI : 10.1007/s00440-004-0411-6

S. Evans and A. Winter, Subtree prune and regraft: A reversible real tree-valued Markov process, The Annals of Probability, vol.34, issue.3, pp.918-961, 2006.
DOI : 10.1214/009117906000000034

N. Gantert, Y. Peres, and Z. Shi, The infinite valley for a recurrent random walk in random environment, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.2
DOI : 10.1214/09-AIHP205
URL : https://hal.archives-ouvertes.fr/hal-00485283

A. O. Golosov, Limit distributions for random walks in random environments, Soviet. Math. Dokl, vol.28, pp.18-22, 1983.

P. Greenwood and J. Pitman, Fluctuation identities for l??vy processes and splitting at the maximum, Advances in Applied Probability, vol.XIV, issue.04, pp.893-902, 1980.
DOI : 10.1090/S0002-9947-1977-0433606-6

A. Grimvall, On the Convergence of Sequences of Branching Processes, The Annals of Probability, vol.2, issue.6, pp.1027-1045, 1974.
DOI : 10.1214/aop/1176996496

B. Haas and G. Miermont, The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree, Electronic Journal of Probability, vol.9, issue.0, pp.57-97, 2004.
DOI : 10.1214/EJP.v9-187
URL : https://hal.archives-ouvertes.fr/hal-00000995

I. S. Helland, Continuity of a class of random time transformations, Stochastic Processes and their Applications, vol.7, issue.1, pp.79-99, 1978.
DOI : 10.1016/0304-4149(78)90040-6

Y. Hu, Tightness of localization and return time in random environment, Stochastic Processes and their Applications, vol.86, issue.1, pp.1477-1521, 2000.
DOI : 10.1016/S0304-4149(99)00087-3

Y. Hu and Z. Shi, The local time of simple random walk in random environment, Journal of Theoretical Probability, vol.11, issue.3, pp.765-793, 1997.
DOI : 10.1023/A:1022658732480

Y. Hu and Z. Shi, The limits of Sinai's simple random walk in random environment, Ann. Probab, vol.26, pp.1477-1521, 1998.

Y. Hu and Z. Shi, 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

Y. Hu, Z. Shi, and M. , YOR Rates of convergence of diffusions with drifted Brownian potentials, Transactions of the American Mathematical Society, vol.351, issue.10, pp.3915-3934, 1999.
DOI : 10.1090/S0002-9947-99-02421-6

J. Jacod, Calcul stochastique etprobì emes de martingales, Lecture Notes in Mathematics, vol.714, 1979.

M. Jirina, Stochastic branching processes with continuous state space, Czech. Math. J, vol.8, pp.292-312, 1958.

K. Kawazu, Y. Tamura, and H. Tanaka, Localization of diffusion processes in one-dimensional random environment, Journal of the Mathematical Society of Japan, vol.44, issue.3, pp.515-555, 1992.
DOI : 10.2969/jmsj/04430515

K. Kawazu and H. Tanaka, A diffusion process in a Brownian environment with drift, J. Math. Soc. Japan, vol.49, pp.189-211, 1997.
DOI : 10.1142/9789812778550_0028

H. Kesten, The limit distribution of Sinai's random walk in random environment, Physica A: Statistical Mechanics and its Applications, vol.138, issue.1-2, pp.99-309, 1986.
DOI : 10.1016/0378-4371(86)90186-X

H. Kesten, M. Koslov, and F. Spitzer, A limit law for random walk in a random environment, Compositio Mathematica, vol.30, pp.145-168, 1975.

J. F. Kingman, The coalescent. Stoch, Proc. App, pp.235-248, 1982.

F. B. Knight, Random walks and a sojourn density process of Brownian motion, Transactions of the American Mathematical Society, vol.109, issue.1, pp.56-86, 1963.
DOI : 10.1090/S0002-9947-1963-0154337-6

J. Lamperti, Continuous state branching processes, Bulletin of the American Mathematical Society, vol.73, issue.3, pp.382-386, 1967.
DOI : 10.1090/S0002-9904-1967-11762-2

J. Lamperti, The Limit of a Sequence of Branching Processes, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.35, issue.4, pp.271-288, 1967.
DOI : 10.1007/BF01844446

J. Gall, A class of path-valued Markov processes and its applications to superprocesses, Probability Theory and Related Fields, vol.8, issue.1, pp.25-46, 1993.
DOI : 10.1007/BF01197336

J. Gall, The uniform random tree in a Brownian excursion, Probability Theory and Related Fields, vol.19, issue.3, pp.369-383, 1993.
DOI : 10.1007/BF01292678

J. Gall, A Path-Valued Markov Process and its Connections with Partial Differential Equations, Proc. First Euro. Congress Math, pp.185-212, 1994.
DOI : 10.1007/978-3-0348-9112-7_8

J. Gall, The Brownian snake and solutions of ??u=u 2 in a domain, Probability Theory and Related Fields, vol.74, issue.3, pp.393-432, 1995.
DOI : 10.1007/BF01192468

J. Gall, Spatial branching processes, random snakes and partial differential equations, 1999.
DOI : 10.1007/978-3-0348-8683-3

J. Gall, Random trees and applications, Probability surveys, pp.245-311, 2005.
DOI : 10.1214/154957805100000140

J. Gall, Y. Le, J. Gall, Y. Le, and . Jan, Branching processes in Lévy processes : Laplace functionals of snake and superprocesses Branching processes in Lévy processes : The exploration process, Ann. Probab. Ann. Probab, vol.26, issue.26, pp.1407-1432, 1998.

H. P. Mckean, Excursions of a non-singular diffusion, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.3, issue.3, pp.230-239, 1963.
DOI : 10.1007/BF00532494

G. Miermont, Self-similar fragmentations derived from the stable tree I, Probability Theory and Related Fields, vol.127, issue.3, pp.423-454, 2003.
DOI : 10.1007/s00440-003-0295-x
URL : https://hal.archives-ouvertes.fr/hal-00001550

G. Miermont, Self-similar fragmentations derived from the stable tree II: splitting at nodes, Probability Theory and Related Fields, vol.92, issue.3, pp.341-375, 2005.
DOI : 10.1007/s00440-004-0373-8
URL : https://hal.archives-ouvertes.fr/hal-00001551

J. Neveu, Arbres et processus de Galton-Watson, Ann. Inst. Henri Poincaré, vol.22, pp.199-207, 1986.

J. Neveu and J. Pitman, Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion, Lecture Notes in Mathematics, vol.27, pp.239-247, 1989.
DOI : 10.1137/1127028

J. Neveu and J. W. Pitman, The branching process in a Brownian excursion, Lecture Notes in Mathematics, vol.28, issue.53, pp.248-257, 1989.
DOI : 10.1112/plms/s3-28.4.738

J. W. Pitman, Coalescents With Multiple Collisions, The Annals of Probability, vol.27, issue.4, 1870.
DOI : 10.1214/aop/1022677552

P. Protter, Stochastic integration and stochastic differential equations : a new approach, Applications Math, 1990.

P. Revesz, Random walk in random and non-random environments, World Scientific, 2005.

L. C. Rogers, A new identity for real Lévy processes, Ann. Inst. Henri Poincaré, vol.20, issue.1, pp.21-34, 1984.

S. Schumacher, Diffusions with random coefficients, Contemp. Math, vol.41, pp.1206-1218, 1986.
DOI : 10.1090/conm/041/814724

Z. Shi, Sinai's walk via stochastic calculus, pp.53-74, 2001.

Z. Shi, 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

Y. G. Sinai, 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

Y. G. Sinai, A Random Walk with Random Potential, Theory of Probability & Its Applications, vol.38, issue.2, pp.382-385, 1985.
DOI : 10.1137/1138036

A. Singh, Limiting behavior of a diffusion in an asymptotically stable environment, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.43, issue.1, pp.101-138, 2007.
DOI : 10.1016/j.anihpb.2006.01.003
URL : https://hal.archives-ouvertes.fr/hal-00004913

A. Singh, 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

F. Solomon, Random Walks in a Random Environment, The Annals of Probability, vol.3, issue.1, pp.1-31, 1975.
DOI : 10.1214/aop/1176996444

M. Talet, 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

H. Tanaka, Limit distributions for one-dimensional diffusion processes in self-similar random environments, in hydrodynamic behavior and interacting particle systems, Math. Appl, vol.9, pp.189-210, 1987.

H. Tanaka, Limit theorem for one-dimensional diffusion process in brownian environment, Lectures Notes in Mathematics, vol.28, issue.3, pp.156-172, 1988.
DOI : 10.1112/plms/s3-28.4.738

H. Tanaka, Localization of a Diffusion Process in a One-Dimensional Brownian Environmement, Comm. Pure Appl. Math, vol.17, pp.755-766, 1994.

H. Tanaka, 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

H. Tanaka, Lévy processes conditionned to stay positive and diffusions in random environments . Stoch. Analysis on Large Scale Inter, Systems. Math. Soc. Japan, vol.39, pp.355-376, 2004.

G. Voisin, Dislocation measure of the fragmentation of a general Lévy tree. prépublication