K. B. Athreya and P. E. Ney, Branching processes, 1972.
DOI : 10.1007/978-3-642-65371-1

J. Bertoin, Exponential decay and ergodicity of completely asymmetric L??vy processes in a finite interval, The Annals of Applied Probability, vol.7, issue.1, pp.156-169, 1997.
DOI : 10.1214/aoap/1034625257

J. Bertoin, Renewal Theory for Embedded Regenerative Sets, The Annals of Probability, vol.27, issue.3, pp.1523-1535, 1999.
DOI : 10.1214/aop/1022677457

J. Bertoin, L. Gall, and J. F. , The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Probab. Theory Relat, pp.249-266, 2000.

J. Bertoin and J. Pitman, Two Coalescents Derived from the Ranges of Stable Subordinators, Electronic Journal of Probability, vol.5, issue.0, 2000.
DOI : 10.1214/EJP.v5-63

N. Bingham, C. Goldie, and J. L. Teugels, Regular variation, 1987.
DOI : 10.1017/CBO9780511721434

E. Bolthausen and A. S. Sznitman, On Ruelle's Probability Cascades and an Abstract Cavity Method, Communications in Mathematical Physics, vol.197, issue.2, pp.247-276, 1998.
DOI : 10.1007/s002200050450

L. Chaumont, Sur certains processus de l??vy conditionn??s ?? rester positifs, Stochastics An International Journal of Probability and Stochastic Processes, vol.47, issue.1, pp.1-20, 1994.
DOI : 10.1080/17442509408833880

W. E. Feller, An Introduction to Probability Theory and Its Applications 2, 1971.

P. J. Fitzsimmons, B. E. Fristedt, and L. A. Shepp, The set of real numbers left uncovered by random covering intervals, Zeitschrift f??r Wahrscheinlichkeitstheorie und verwandte Gebiete, vol.52, issue.2, pp.175-189, 1985.
DOI : 10.1007/BF02451427

F. B. Knight, Brownian local times and taboo processes, Transactions of the American Mathematical Society, vol.143, pp.173-185, 1969.
DOI : 10.1090/S0002-9947-1969-0253424-7

A. Lambert, Completely asymmetric L????vy processes confined in a finite interval, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.36, issue.2, pp.251-274, 2000.
DOI : 10.1016/S0246-0203(00)00126-6

A. Lambert, The genealogy of continuous-state branching processes with immigration, Probability Theory and Related Fields, vol.122, issue.1, 2000.
DOI : 10.1007/s004400100155

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

L. Gall, J. F. , L. Jan, and Y. , Branching processes in L??vy processes: the exploration process, The Annals of Probability, vol.26, issue.1, pp.213-252, 1998.
DOI : 10.1214/aop/1022855417

R. Lyons, R. Pemantle, and Y. Peres, Conceptual Proofs of $L$ Log $L$ Criteria for Mean Behavior of Branching Processes, The Annals of Probability, vol.23, issue.3, pp.1125-1138, 1995.
DOI : 10.1214/aop/1176988176

J. Pitman, Coalescents With Multiple Collisions, The Annals of Probability, vol.27, issue.4, pp.1870-1902, 1999.
DOI : 10.1214/aop/1022677552

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.8043

N. U. Prabhu, Stochastic Storage Processes, Queues, Insurance Risk and Dams, 1981.

L. Takács, Combinatorial Methods in the Theory of Stochastic Processes, 1966.

J. Bertoin, An Extension of Pitman's Theorem for Spectrally Positive Levy Processes, The Annals of Probability, vol.20, issue.3, pp.1464-1483, 1992.
DOI : 10.1214/aop/1176989701

J. Bertoin, Lévy processes, 1996.

J. Bertoin, On the First Exit Time of a Completely Asymmetric Stable Process from a Finite Interval, Bulletin of the London Mathematical Society, vol.28, issue.5, pp.514-520, 1996.
DOI : 10.1112/blms/28.5.514

J. Bertoin, Exponential decay and ergodicity of completely asymmetric L??vy processes in a finite interval, The Annals of Applied Probability, vol.7, issue.1, pp.156-169, 1997.
DOI : 10.1214/aoap/1034625257

J. Bertoin, Cauchy's Principal Value of Local Times of L??vy Processes with no Negative Jumps via Continuous Branching Processes, Electronic Journal of Probability, vol.2, issue.0, pp.1-12, 1997.
DOI : 10.1214/EJP.v2-20

N. H. Bingham, Fluctuation theory in continuous time, Advances in Applied Probability, vol.7, issue.04, pp.705-766, 1975.
DOI : 10.1137/1110038

N. H. Bingham, Continuous branching processes and spectral positivity, Stochastic Processes and their Applications, vol.4, issue.3, pp.217-242, 1976.
DOI : 10.1016/0304-4149(76)90011-9

A. A. Borovkov, Stochastic Processes in Queuing Theory, 1976.

C. Dellacherie, P. A. Meyer, and B. Maisonneuve, Probabilités et Potentiel (tome 5), 1992.

D. J. Emery, Exit problem for a spectrally positive process, Advances in Applied Probability, vol.5, issue.03, pp.498-520, 1973.
DOI : 10.1137/1114002

D. R. Grey, Asymptotic behaviour of continuous time, continuous state-space branching processes, Journal of Applied Probability, vol.17, issue.04, pp.669-677, 1974.
DOI : 10.1090/S0002-9947-1969-0234531-1

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

F. B. Knight, Brownian local times and taboo processes, Transactions of the American Mathematical Society, vol.143, pp.173-185, 1969.
DOI : 10.1090/S0002-9947-1969-0253424-7

A. Lambert, Completely asymmetric L????vy processes confined in a finite interval, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.36, issue.2, pp.251-274, 1999.
DOI : 10.1016/S0246-0203(00)00126-6

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

L. Gall, J. F. , L. Jan, and Y. , Branching processes in L??vy processes: the exploration process, The Annals of Probability, vol.26, issue.1, pp.213-252, 1998.
DOI : 10.1214/aop/1022855417

N. U. Prabhu, Stochastic Storage Processes, Queues, Insurance Risk and Dams, 1981.

H. Robbins and D. Siegmund, On the law of the iterated logarithm for maxima and minima, Proc. Sixth Berkeley Symp, pp.51-70, 1972.

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

L. C. Rogers, A Guided Tour through Excursions, Bulletin of the London Mathematical Society, vol.21, issue.4, pp.305-341, 1989.
DOI : 10.1112/blms/21.4.305

L. C. Rogers, The two-sided exit problem for spectrally positive L??vy processes, Advances in Applied Probability, vol.22, issue.02, pp.486-487, 1990.
DOI : 10.2307/1426397

V. N. Suprun, Problem of desteuction and resolvent of a terminating process with independent increments, Ukrainian Mathematical Journal, vol.28, issue.1, pp.39-45, 1976.
DOI : 10.1007/BF01559226

E. Seneta and D. Vere-jones, On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states, Journal of Applied Probability, vol.1, issue.02, pp.403-434, 1966.
DOI : 10.1093/qmath/13.1.7

L. Takács, Combinatorial Methods in the Theory of Stochastic Processes, 1966.

P. Tuominen and R. L. Tweedie, Exponential decay and ergodicity of general Markov processes and their discrete skeletons, Advances in Applied Probability, vol.13, issue.04, pp.784-803, 1979.
DOI : 10.2307/1426143

D. Vere-jones, Ergodic properties of non-negative matrices, Pac. J. Math, vol.28, issue.22, pp.361-386, 1967.

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

J. Bertoin, An Extension of Pitman's Theorem for Spectrally Positive Levy Processes, The Annals of Probability, vol.20, issue.3, pp.1464-1483, 1992.
DOI : 10.1214/aop/1176989701

J. Bertoin, Splitting at the infimum and excursions in half-lines for random walks and L??vy processes, Stochastic Processes and their Applications, vol.47, issue.1, pp.17-35, 1993.
DOI : 10.1016/0304-4149(93)90092-I

J. Bertoin, Lévy processes, 1996.

J. Bertoin, Exponential decay and ergodicity of completely asymmetric L??vy processes in a finite interval, The Annals of Applied Probability, vol.7, issue.1, pp.156-169, 1997.
DOI : 10.1214/aoap/1034625257

J. Bertoin, L. Gall, and J. F. , The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes, 1999.

N. H. Bingham, Fluctuation theory in continuous time, Advances in Applied Probability, vol.7, issue.04, pp.705-766, 1975.
DOI : 10.1137/1110038

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

L. Chaumont, Sur certains processus de l??vy conditionn??s ?? rester positifs, Stochastics An International Journal of Probability and Stochastic Processes, vol.47, issue.1, pp.1-20, 1994.
DOI : 10.1080/17442509408833880

L. Chaumont, Conditionings and path decompositions for L??vy processes, Stochastic Processes and their Applications, vol.64, issue.1, pp.39-54, 1996.
DOI : 10.1016/S0304-4149(96)00081-6

K. Itô, Poisson point processes attached to Markov processes, Proc. Sixth Berkeley Symp, pp.225-240, 1971.

K. Itô, H. P. Mckean, and . Jr, Diffusion Processes and their Sample Paths, 1974.

K. Kawazu and S. Watanabe, Branching Processes with Immigration and Related Limit Theorems, Theory of Probability & Its Applications, vol.16, issue.1, pp.34-51, 1971.
DOI : 10.1137/1116003

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

L. Gall, J. F. , L. Jan, and Y. , Branching processes in L??vy processes: the exploration process, The Annals of Probability, vol.26, issue.1, pp.213-252, 1998.
DOI : 10.1214/aop/1022855417

L. Gall, J. F. , L. Jan, and Y. , Branching processes in Lévy processes : Laplace functionals of snakes and Lévy processes, Ann. Probab, vol.26, pp.1407-1432, 1998.

L. Gall, J. F. Yor, and M. , Excursions browniennes et carrés de processus de Bessel, CRAS (Série I) vol, vol.103, pp.73-76, 1986.

P. W. Millar, Zero-one laws and the minimum of a Markov process, Transactions of the American Mathematical Society, vol.226, pp.365-391, 1977.
DOI : 10.1090/S0002-9947-1977-0433606-6

M. A. Pinsky, Limit theorems for continuous state branching processes with immigration, Bulletin of the American Mathematical Society, vol.78, issue.2, pp.242-244, 1972.
DOI : 10.1090/S0002-9904-1972-12938-0

J. W. Pitman, One-dimensional Brownian motion and the three-dimensional Bessel process, Advances in Applied Probability, vol.85, issue.03, pp.511-526, 1975.
DOI : 10.1090/S0002-9904-1970-12591-5

L. C. Rogers, It??? excursion theory via resolvents, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.40, issue.53, pp.237-255, 1983.
DOI : 10.1007/BF00538964

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

T. S. Salisbury, On the It??? excursion process, Probability Theory and Related Fields, vol.5, issue.4, pp.319-350, 1986.
DOI : 10.1007/BF00776237

T. S. Salisbury, Construction of right processes from excursions, Probability Theory and Related Fields, vol.52, issue.53, pp.351-367, 1986.
DOI : 10.1007/BF00776238

D. Williams, Diffusions, Markov Processes, and Martingales, 1979.

K. B. Athreya and P. E. Ney, Branching processes, 1972.
DOI : 10.1007/978-3-642-65371-1

N. H. Bingham, Continuous branching processes and spectral positivity, Stochastic Processes and their Applications, vol.4, issue.3, pp.217-242, 1976.
DOI : 10.1016/0304-4149(76)90011-9

L. Chaumont, Conditionings and path decompositions for L??vy processes, Stochastic Processes and their Applications, vol.64, issue.1, pp.39-54, 1996.
DOI : 10.1016/S0304-4149(96)00081-6

D. R. Grey, Asymptotic behaviour of continuous time, continuous state-space branching processes, Journal of Applied Probability, vol.17, issue.04, pp.669-677, 1974.
DOI : 10.1090/S0002-9947-1969-0234531-1

O. Kallenberg, Some time change representations of stable integrals, via predictable transformations of local martingales, Stochastic Processes and their Applications, vol.40, issue.2, pp.199-223, 1992.
DOI : 10.1016/0304-4149(92)90012-F

A. Lambert, The genealogy of continuous-state branching processes with immigration, Prépublication 555 du Laboratoire de Probabilités et Modèles Aléatoires, U. P. et M. Curie, 1999.
DOI : 10.1007/s004400100155

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

L. Gall, J. F. , L. Jan, and Y. , Branching processes in L??vy processes: the exploration process, The Annals of Probability, vol.26, issue.1, pp.213-252, 1998.
DOI : 10.1214/aop/1022855417

R. Lyons, R. Pemantle, and Y. Peres, Conceptual Proofs of $L$ Log $L$ Criteria for Mean Behavior of Branching Processes, The Annals of Probability, vol.23, issue.3, pp.1125-1138, 1995.
DOI : 10.1214/aop/1176988176

M. A. Pinsky, Limit theorems for continuous state branching processes with immigration, Bulletin of the American Mathematical Society, vol.78, issue.2, pp.242-244, 1972.
DOI : 10.1090/S0002-9904-1972-12938-0

P. A. Zanzotto, On stochastic differential equations driven by Cauchy process and the other ?-stable, 1999.

J. Bertoin, Subordinators : examples and applications. Cours de l' ´ Ecole d'´ eté de Probabilités de St-Flour, 1999.

J. Bertoin, Renewal Theory for Embedded Regenerative Sets, The Annals of Probability, vol.27, issue.3, pp.1523-1535, 1999.
DOI : 10.1214/aop/1022677457

J. Bertoin, Intersection of independent regenerative sets. Probab. Theory Relat, pp.97-121, 1999.

J. Bertoin, L. Gall, and J. F. , The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Probab. Theory Relat, pp.249-266, 2000.

J. Bertoin and J. Pitman, Two Coalescents Derived from the Ranges of Stable Subordinators, Electronic Journal of Probability, vol.5, issue.0, 2000.
DOI : 10.1214/EJP.v5-63

N. Bingham, C. Goldie, and J. L. Teugels, Regular variation, 1987.
DOI : 10.1017/CBO9780511721434

E. Bolthausen and A. S. Sznitman, On Ruelle's Probability Cascades and an Abstract Cavity Method, Communications in Mathematical Physics, vol.197, issue.2, pp.247-276, 1998.
DOI : 10.1007/s002200050450

O. Chateau, Quelques remarques sur la subordination au sens de Bochner, Thèse de l, 1990.

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

W. E. Feller, An Introduction to Probability Theory and Its Applications 2, 1971.

P. J. Fitzsimmons and M. I. Taksar, Stationary Regenerative Sets and Subordinators, The Annals of Probability, vol.16, issue.3, pp.1299-1305, 1988.
DOI : 10.1214/aop/1176991692

P. J. Fitzsimmons, B. E. Fristedt, and L. A. Shepp, The set of real numbers left uncovered by random covering intervals, Zeitschrift f??r Wahrscheinlichkeitstheorie und verwandte Gebiete, vol.52, issue.2, pp.175-189, 1985.
DOI : 10.1007/BF02451427

B. E. Fristedt, Sample functions of stochastic processes with stationary, independent increments, In : Advances in Probability, vol.3, pp.241-396, 1974.

B. E. Fristedt, Intersections and Limits of Regenerative Sets, pp.121-151, 1996.
DOI : 10.1007/978-1-4612-0719-1_9

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 1980.

J. Hawkes, Intersections of Markov random sets, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.65, issue.3, pp.243-251, 1977.
DOI : 10.1007/BF00537491

J. F. Kingman, The coalescent, Stochastic Processes and their Applications, vol.13, issue.3, pp.235-248, 1982.
DOI : 10.1016/0304-4149(82)90011-4

G. Matheron, Random sets and integral geometry, 1975.

J. Pitman, Partition Structures Derived from Brownian Motion and Stable Subordinators, Bernoulli, vol.3, issue.1, pp.79-96, 1997.
DOI : 10.2307/3318653

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.4369

J. Pitman, Coalescents With Multiple Collisions, The Annals of Probability, vol.27, issue.4, pp.1870-1902, 1999.
DOI : 10.1214/aop/1022677552

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.8043

J. Pitman and M. Yor, Arcsine Laws and Interval Partitions Derived from a Stable Subordinator, Proc. London Math. Soc. 65, pp.326-356, 1992.
DOI : 10.1112/plms/s3-65.2.326

D. Ruelle, A mathematical reformulation of Derrida's REM and GREM, Communications in Mathematical Physics, vol.35, issue.2, pp.225-239, 1987.
DOI : 10.1007/BF01210613

M. I. Taksar, Stationary Markov sets, pp.303-340, 1998.
DOI : 10.1007/BF00533723

S. Watanabe, On time inversion of one-dimensional diffusion processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.26, issue.4, pp.115-124, 1975.
DOI : 10.1007/BF00539436