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 cois},
     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}
}
Duquesne, Thomas; Le Gall, Jean-François. Random trees, Lévy processes and spatial branching processes. Astérisque, no. 281 (2002), 153 p. http://www.numdam.org/item/AST_2002__281__R1_0/

[1] Aldous, D. (1991) The continuum random tree I. Ann. Probab. 19, 1-28. | Article | MR 1085326 | Zbl 0722.60013

[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. | Article | MR 1166406 | Zbl 0791.60008

[3] Aldous, D. (1993) The continuum random tree III. Ann. Probab. 21, 248-289. | Article | MR 1207226 | Zbl 0791.60009

[4] Bennies, J., Kersting, G. (2000) A random walk approach to Galton-Watson trees. J. Theoret. Probab. 13, 777-803. | Article | MR 1785529 | Zbl 0977.60083

[5] Bertoin, J. (1996) Lévy Processes. Cambridge University Press, Cambridge. | MR 1406564 | Zbl 0938.60005

[6] Bingham, N. (1975) Fluctuation theory in continuous time. Adv. Appl. Probab. 7, 705-766. | Article | MR 386027 | Zbl 0322.60068

[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. | Article | MR 1401459 | Zbl 0869.60077

[8] Dawson, D. A., Perkins, E. A. (1991) Historical Processes. Memoirs Amer. Math. Soc. 454. | MR 1079034 | Zbl 0754.60062

[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 898005 | Zbl 0624.60084

[10] Duquesne, T. (2001) A limit theorem for the contour process of conditioned Galton-Watson trees. Ann. Probab., to appear. | MR 1964956 | Zbl 1025.60017

[11] Dwass, M. (1975) Branching processes in simple random walk. Proc. Amer. Math. Soc. 51, 251-274. | Article | MR 370775 | Zbl 0312.60032

[12] Dynkin, E. B. (1991) A probabilistic approach to one class of nonlinear differential equations. Probab. Th. Rel. Fields 89, 89-115. | Article | MR 1109476 | Zbl 0722.60062

[13] Dynkin, E. B. (2001) Diffusions, Superdiffusions and Partial Differential Equations. Amer. Math. Soc. Colloquium Publications, Vol. 50. Providence, 2002. | MR 1883198 | Zbl 0999.60003

[14] Ethier, S. N., Kurtz, T. (1986) Markov Processes: Characterization and Convergence. Wiley. | MR 838085 | Zbl 1089.60005

[15] Etheridge, A. M. (2000) An Introduction to Superprocesses. University Lecture Series vol. 20. American Math. Society, Providence. | MR 1779100 | Zbl 0971.60053

[16] Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II, 2 sec. ed.. Wiley, New York. | MR 270403

[17] Fleischmann, K., Siegmund-Schultze, R. (1977) The structure of reduced critical Galton-Watson processes. Math. Nachr. 79, 233-241. | Article | MR 461689 | Zbl 0299.60065

[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. | Article | MR 1352736 | Zbl 0823.60077

[19] Gittenberger, B. (1999) On the contour of random trees. SIAM J. Discrete Math. 12, 434-458. | Article | MR 1720416 | Zbl 0935.05032

[20] Grey, D. R. (1974) Asymptotic behaviour of continuous time, continuous statespace branching processes. J. Appl. Probab. 11, 669-677. | Article | MR 408016 | Zbl 0301.60060

[21] Grimvall, A. (1974) On the convergence of sequence of branching processes. Ann. Probab. 2, 1027-1945. | Article | MR 362529 | Zbl 0361.60062

[22] Hobson, D. G. (2000) Marked excursions and random trees. Séminaire de Probabilités XXXIV. Lecture Notes Math. 1729, pp. 289-301. Springer. | Article | Numdam | MR 1768069 | Zbl 0965.60078

[23] Jacod, J. (1985) Théorèmes limites pour les processus. Lecture Notes in Math. 1117, 298-409. Springer, Berlin. | MR 883648 | Zbl 0565.60030

[24] Jacod, J., Shiryaev, A. N. (1987) Limit Theorems for Stochastic Processes. Springer, Berlin. | Article | MR 959133 | Zbl 0635.60021

[25] Keller, J. B. (1957) On solutions of Δu=f(u). Comm. Pure Appl. Math. 10, 503-510. | MR 91407 | Zbl 0090.31801

[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. | Article | MR 217893 | Zbl 0154.42603

[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. | Article | MR 1207305 | Zbl 0794.60076

[29] Le Gall, J. F. (1994) Hitting probabilities and potential theory for the Brownian path-valued process. Ann. Inst. Fourier 44, 277-306. | Article | Numdam | MR 1262889 | Zbl 0794.60077

[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. | Article | MR 1339740 | Zbl 0826.60062

[31] Le Gall, J. F. (1999) Spatial Branching Processes, Random Snakes and Partial Differential Equations. Birkhaüser, Boston. | MR 1714707 | Zbl 0938.60003

[32] Le Gall, J. F., Le Jan, Y. (1998) Branching processes in Lévy processes: The exploration process. Ann. Probab. 26, 213-252. | Article | MR 1617047 | Zbl 0948.60071

[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. | MR 1675019 | Zbl 0945.60090

[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. | Article | MR 1379165 | Zbl 0856.60055

[35] Limic, V. (2001) A LIFO queue in heavy traffic. Ann. Appl. Probab. 11, 301-331. | Article | MR 1843048 | Zbl 1015.60079

[36] Marckert, J. F., Mokkadem, A. (2001) The depth first processes of Galton-Watson trees converge to the same Brownian excursion. Preprint. | MR 1989446 | Zbl 1049.05026

[37] Mejzler, D. (1973) On a certain class of infinitely divisible distributions. Israel J. Math. 16, 1-19. | Article | MR 350808 | Zbl 0276.60022

[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. | Article | Numdam | MR 1022915 | Zbl 0741.60081

[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. | MR 1915445 | Zbl 1020.60075

[41] Osserman, R. (1957) On the inequality Δuf(u). Pac. J. Math. 7, 1641-1647. | MR 98239 | Zbl 0083.09402

[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 | MR 770947 | Zbl 0542.60080

[43] Salisbury, T. S., Verzani, F. (1999) On the conditioned exit measures of super-Brownian motion. Probab. Th. Rel. Fields 115, 237-285. | Article | MR 1720367 | Zbl 0953.60078

[44] Salisbury, T. S., Verzani, F. (2000) Non-degenerate conditionings of the exit measures of super-Brownian motion. Stoch. Process. Appl. 87, 25-52. | Article | MR 1751163 | Zbl 1045.60047

[45] Sheu, Y. C. (1994) Asymptotic behavior of superprocesses. Stochastics Stoch. Reports 49, 239-252. | Article | MR 1785007 | Zbl 0827.60066

[46] Skorokhod (1957) Limit theorems for stochastic processes with independent increments. Theory Probab. Appl. 2, 138-171. | Article | MR 94842 | Zbl 0097.13001

[47] Slack, R. S. (1968) A branching process with mean one and possibly infinite variance. Z. Wahrsch. verw. Gebiete 9, 139-145. | Article | MR 228077 | Zbl 0164.47002

[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. | Article | MR 443115 | Zbl 0396.60072

[49] Yakymiv, A. L. (1980) Reduced branching processes. Theory Probab. Appl. 25, 584-588. | Article | MR 582588 | Zbl 0463.60070

[50] Zubkov, A. M. (1975) Limit distributions of the distance to the closest common ancestor. Theory Probab. Appl. 20, 602-612. | Article | MR 397915 | Zbl 0348.60118