Random trees, Lévy processes and spatial branching processes
Astérisque, no. 281 (2002) , 153 p.
@book{AST_2002__281__R1_0,
     author = {Duquesne, Thomas and Le Gall, Jean-Fran\c{c}ois},
     title = {Random trees, {L\'evy} processes and spatial branching processes},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {281},
     year = {2002},
     zbl = {1037.60074},
     mrnumber = {1954248},
     language = {en},
     url = {http://www.numdam.org/item/AST_2002__281__R1_0/}
}
TY  - BOOK
AU  - Duquesne, Thomas
AU  - Le Gall, Jean-François
TI  - Random trees, Lévy processes and spatial branching processes
T3  - Astérisque
PY  - 2002
DA  - 2002///
IS  - 281
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2002__281__R1_0/
UR  - https://zbmath.org/?q=an%3A1037.60074
UR  - https://www.ams.org/mathscinet-getitem?mr=1954248
LA  - en
ID  - AST_2002__281__R1_0
ER  - 
%0 Book
%A Duquesne, Thomas
%A Le Gall, Jean-François
%T Random trees, Lévy processes and spatial branching processes
%S Astérisque
%D 2002
%N 281
%I Société mathématique de France
%G en
%F AST_2002__281__R1_0
Duquesne, Thomas; Le Gall, Jean-François. Random trees, Lévy processes and spatial branching processes. Astérisque, no. 281 (2002), 153 p. http://numdam.org/item/AST_2002__281__R1_0/

[1] Aldous, D. (1991) The continuum random tree I. Ann. Probab. 19, 1-28. | DOI | Zbl | MR

[2] Aldous, D. (1991) The continuum random tree II: An overview. In: Stochastic Analysis (M.T. Barlow, N.H. Bingham eds), pp. 23-70. Cambridge University Press, Cambridge. | DOI | Zbl | MR

[3] Aldous, D. (1993) The continuum random tree III. Ann. Probab. 21, 248-289. | DOI | Zbl | MR

[4] Bennies, J., Kersting, G. (2000) A random walk approach to Galton-Watson trees. J. Theoret. Probab. 13, 777-803. | DOI | Zbl | MR

[5] Bertoin, J. (1996) Lévy Processes. Cambridge University Press, Cambridge. | Zbl | MR

[6] Bingham, N. (1975) Fluctuation theory in continuous time. Adv. Appl. Probab. 7, 705-766. | DOI | Zbl | MR

[7] Borovkov, K. A., Vatutin, V. A. (1996) On distribution tails and expectations of maxima in critical branching processes. J. Appl. Probab. 33, 614-622. | DOI | Zbl | MR

[8] Dawson, D. A., Perkins, E. A. (1991) Historical Processes. Memoirs Amer. Math. Soc. 454. | Zbl | MR

[9] Dellacherie, C, Meyer, P. A. (1987) Probabilités et potentiels, Chapitres XII à XVI: Théorie du potentiel associée une résolvante, théorie des processus de Markov. Hermann, Paris | MR | Zbl

[10] Duquesne, T. (2001) A limit theorem for the contour process of conditioned Galton-Watson trees. Ann. Probab., to appear. | Zbl | MR

[11] Dwass, M. (1975) Branching processes in simple random walk. Proc. Amer. Math. Soc. 51, 251-274. | DOI | Zbl | MR

[12] Dynkin, E. B. (1991) A probabilistic approach to one class of nonlinear differential equations. Probab. Th. Rel. Fields 89, 89-115. | DOI | Zbl | MR

[13] Dynkin, E. B. (2001) Diffusions, Superdiffusions and Partial Differential Equations. Amer. Math. Soc. Colloquium Publications, Vol. 50. Providence, 2002. | Zbl | MR

[14] Ethier, S. N., Kurtz, T. (1986) Markov Processes: Characterization and Convergence. Wiley. | Zbl | MR

[15] Etheridge, A. M. (2000) An Introduction to Superprocesses. University Lecture Series vol. 20. American Math. Society, Providence. | Zbl | MR

[16] Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II, 2 sec. ed.. Wiley, New York. | MR

[17] Fleischmann, K., Siegmund-Schultze, R. (1977) The structure of reduced critical Galton-Watson processes. Math. Nachr. 79, 233-241. | DOI | Zbl | MR

[18] Geiger, J. (1995) Contour processes of random trees. In: Stochastic Partial Differential Equations (A. Etheridge ed.). London Math. Soc. Lect. Notes 216, pp. 72-96. Cambridge University Press, Cambridge. | DOI | Zbl | MR

[19] Gittenberger, B. (1999) On the contour of random trees. SIAM J. Discrete Math. 12, 434-458. | DOI | Zbl | MR

[20] Grey, D. R. (1974) Asymptotic behaviour of continuous time, continuous statespace branching processes. J. Appl. Probab. 11, 669-677. | DOI | Zbl | MR

[21] Grimvall, A. (1974) On the convergence of sequence of branching processes. Ann. Probab. 2, 1027-1945. | DOI | Zbl | MR

[22] Hobson, D. G. (2000) Marked excursions and random trees. Séminaire de Probabilités XXXIV. Lecture Notes Math. 1729, pp. 289-301. Springer. | DOI | Numdam | EuDML | Zbl | MR

[23] Jacod, J. (1985) Théorèmes limites pour les processus. Lecture Notes in Math. 1117, 298-409. Springer, Berlin. | Zbl | MR

[24] Jacod, J., Shiryaev, A. N. (1987) Limit Theorems for Stochastic Processes. Springer, Berlin. | DOI | Zbl | MR

[25] Keller, J. B. (1957) On solutions of Δu=f(u). Comm. Pure Appl. Math. 10, 503-510. | Zbl | MR

[26] Kersting, G. (1998) On the height profile of a conditioned Galton-Watson tree. To appear.

[27] Lamperti, J. (1967) The limit of a sequence of branching processes. Z. Wahrsch. verw. Gebiete 7, 271-288. | DOI | Zbl | MR

[28] Le Gall, J. F. (1993) A class of path-valued Markov processes and its applications to superprocesses. Probab. Th. Rel. Fields 95, 25-46. | DOI | Zbl | MR

[29] Le Gall, J. F. (1994) Hitting probabilities and potential theory for the Brownian path-valued process. Ann. Inst. Fourier 44, 277-306. | DOI | Numdam | EuDML | Zbl | MR

[30] Le Gall, J. F. (1995) The Brownian snake and solutions of Δu=u 2 in a domain. Probab. Th. Rel. Fields 102, 393-432. | DOI | Zbl | MR

[31] Le Gall, J. F. (1999) Spatial Branching Processes, Random Snakes and Partial Differential Equations. Birkhaüser, Boston. | Zbl | MR

[32] Le Gall, J. F., Le Jan, Y. (1998) Branching processes in Lévy processes: The exploration process. Ann. Probab. 26, 213-252. | DOI | Zbl | MR

[33] Le Gall, J. F., Le Jan, Y. (1998) Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses. Ann. Probab. 26, 1407-1432. | Zbl | MR

[34] Le Gall, J. F., Perkins, E. A. (1995) The Hausdorff measure of the support of two-dimensional super-Brownian motion. Ann. Probab. 23, 1719-1747. | DOI | Zbl | MR

[35] Limic, V. (2001) A LIFO queue in heavy traffic. Ann. Appl. Probab. 11, 301-331. | DOI | Zbl | MR

[36] Marckert, J. F., Mokkadem, A. (2001) The depth first processes of Galton-Watson trees converge to the same Brownian excursion. Preprint. | Zbl | MR

[37] Mejzler, D. (1973) On a certain class of infinitely divisible distributions. Israel J. Math. 16, 1-19. | DOI | Zbl | MR

[38] Mselati, B. (2002) Probabilistic classification and representation of positive solutions of Δu=u 2 in a domain. PhD thesis, Université Paris VI.

[39] Neveu, J., Pitman, J. W. (1989) The branching process in a Brownian excursion. Séminaire de Probabilités XXIII. Lecture Notes Math. 1372, pp. 248-257. Springer. | DOI | Numdam | EuDML | Zbl | MR

[40] Perkins, E. A. (1999) Dawson-Watanabe Superprocesses and Measure-valued Diffusions. Notes from the Ecole d'été de probabilités de Saint-Flour 1999. To appear. | Zbl | MR

[41] Osserman, R. (1957) On the inequality Δuf(u). Pac. J. Math. 7, 1641-1647. | Zbl | MR

[42] Rogers, L. C. G. (1984) Brownian local times and branching processes. Séminaire de Probabilités XVIII. Lecture Notes Math. 1059, pp. 42-55. Springer. | Numdam | EuDML | Zbl | MR

[43] Salisbury, T. S., Verzani, F. (1999) On the conditioned exit measures of super-Brownian motion. Probab. Th. Rel. Fields 115, 237-285. | DOI | Zbl | MR

[44] Salisbury, T. S., Verzani, F. (2000) Non-degenerate conditionings of the exit measures of super-Brownian motion. Stoch. Process. Appl. 87, 25-52. | DOI | Zbl | MR

[45] Sheu, Y. C. (1994) Asymptotic behavior of superprocesses. Stochastics Stoch. Reports 49, 239-252. | DOI | Zbl | MR

[46] Skorokhod (1957) Limit theorems for stochastic processes with independent increments. Theory Probab. Appl. 2, 138-171. | DOI | MR | Zbl

[47] Slack, R. S. (1968) A branching process with mean one and possibly infinite variance. Z. Wahrsch. verw. Gebiete 9, 139-145. | DOI | Zbl | MR

[48] Vatutin, V. A. (1977) Limit theorems for critical Markov branching processes with several types of particles and infinite second moments. Math. USSR Sbornik 32, 215-225. | DOI | MR | Zbl

[49] Yakymiv, A. L. (1980) Reduced branching processes. Theory Probab. Appl. 25, 584-588. | DOI | MR | Zbl

[50] Zubkov, A. M. (1975) Limit distributions of the distance to the closest common ancestor. Theory Probab. Appl. 20, 602-612. | DOI | MR | Zbl