A super-stable motion with infinite mean branching
Annales de l'I.H.P. Probabilités et statistiques, Volume 40 (2004) no. 5, p. 513-537
@article{AIHPB_2004__40_5_513_0,
     author = {Fleischmann, Klaus and Sturm, Anja},
     title = {A super-stable motion with infinite mean branching},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {40},
     number = {5},
     year = {2004},
     pages = {513-537},
     doi = {10.1016/j.anihpb.2003.09.004},
     zbl = {1052.60065},
     mrnumber = {2086012},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2004__40_5_513_0}
}
Fleischmann, Klaus; Sturm, Anja. A super-stable motion with infinite mean branching. Annales de l'I.H.P. Probabilités et statistiques, Volume 40 (2004) no. 5, pp. 513-537. doi : 10.1016/j.anihpb.2003.09.004. http://www.numdam.org/item/AIHPB_2004__40_5_513_0/

[1] D. Aldous, Stopping times and tightness, Ann. Probab. 6 (2) (1978) 335-340. | MR 474446 | Zbl 0391.60007

[2] J. Bertoin, J.-F. Le Gall, The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes, Probab. Theory Related Fields 117 (2000) 249-266. | Zbl 0963.60086

[3] E. Bolthausen, A.-S. Sznitman, On Ruelle's probability cascades and an abstract cavity method, Comm. Math. Phys. 197 (2) (1998) 247-276. | MR 1652734 | Zbl 0927.60071

[4] A. Bovier, I. Kurkova, Derrida's generalized random energy models 4: Continuous state branching and coalescents, WIAS Berlin, Preprint 854, 2003. | MR 2013661

[5] D.A. Dawson, Measure-valued Markov processes, in: École d'Été de Probabilités de Saint-Flour XXI, 1991, Lecture Notes in Math., vol. 1541, Springer, Berlin, 1993, pp. 1-260. | MR 1242575 | Zbl 0799.60080

[6] D.A. Dawson, V. Vinogradov, Almost-sure path properties of (2,d,β)-superprocesses, Stochastic Process. Appl. 51 (2) (1994) 221-258. | Zbl 0810.60028

[7] E.B. Dynkin, An Introduction to Branching Measure-Valued Processes, CRM Monograph Series, vol. 6, AMS, 1994. | MR 1280712 | Zbl 0824.60001

[8] N. El Karoui, S. Roelly, Propriétés de martingales, explosion et représentation de Lévy-Khintchine d'une classe de processus de branchement à valeurs mesures, Stochastic Process. Appl. 38 (1991) 239-266. | Zbl 0743.60081

[9] A.M. Etheridge, An Introduction to Superprocesses, University Lecture Series, vol. 20, American Mathematical Society, Providence, RI, 2000. | MR 1779100 | Zbl 0971.60053

[10] S.N. Ethier, T.G. Kurtz, Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics, Wiley, 1986. | MR 838085 | Zbl 0592.60049

[11] P.I. Fitzsimmons, Construction and regularity of measure-valued Markov branching processes, Israel J. Math. 64 (3) (1988) 337-361. | MR 995575 | Zbl 0673.60089

[12] P.I. Fitzsimmons, Corrections to “Construction and regularity of measure-valued Markov branching processes”, Israel J. Math. 73 (1) (1991) 127. | Zbl 0731.60075

[13] K. Fleischmann, Critical behaviour of some measure-valued processes, Math. Nachr. 135 (1988) 131-147. | MR 944225 | Zbl 0655.60071

[14] K. Fleischmann, J. Gärtner, Occupation time processes at a critical point, Math. Nachr. 125 (1986) 275-290. | MR 847367 | Zbl 0596.60080

[15] K. Fleischmann, A. Klenke, The biodiversity of catalytic super-Brownian motion, Ann. Appl. Probab. 10 (1) (2000) 1121-1136. | MR 1810867 | Zbl 1073.60055

[16] K. Fleischmann, L. Mytnik, Regularity and irregularity of densities for super-α-stable motion with Neveu's branching mechanism, WIAS Berlin, Preprint (in preparation), 2004.

[17] K. Fleischmann, V. Vakhtel, Large scale behavior of a spatial version of Neveu's branching process, WIAS Berlin, Preprint (in preparation), 2004.

[18] D.R. Grey, Almost sure convergence in Markov branching processes with infinite mean, J. Appl. Probab. 14 (1977) 702-716. | MR 478377 | Zbl 0378.60064

[19] J. Hale, Ordinary Differential Equations, Wiley-Interscience, New York, 1969. | MR 419901 | Zbl 0186.40901

[20] I. Iscoe, A weighted occupation time for a class of measure-valued branching processes, Probab. Theory Related Fields 71 (1) (1986) 85-116. | MR 814663 | Zbl 0555.60034

[21] A. Jakubowski, On the Skorokhod topology, Ann. Inst. Henri Poincaré 22 (3) (1986) 263-285. | Numdam | MR 871083 | Zbl 0609.60005

[22] O. Kallenberg, Random Measures, Academic Press, 1976. | MR 431373 | Zbl 0345.60032

[23] J.-F. Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Birkhäuser Verlag, Basel, 1999. | MR 1714707 | Zbl 0938.60003

[24] L. Mytnik, E. Perkins, Regularity and irregularity of (1+β)-stable super-Brownian motion, Ann. Probab. 31 (3) (2003) 1413-1440. | Zbl 1042.60030

[25] J. Neveu, A continuous state branching process in relation with the GREM model of spin glasses theory, Rapport Interne no 267, CMP École Polytechnique, 1992.

[26] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44, Springer, Berlin, 1983. | MR 710486 | Zbl 0516.47023

[27] E. Perkins, Dawson-Watanabe superprocesses and measure-valued diffusions, in: Bernard P. (Ed.), École d'été de probabilités de Saint Flour XXIX-1999, Lecture Notes in Mathematics, vol. 1781, Berlin, Springer, 2002, pp. 125-329. | Zbl 1020.60075

[28] J. Pitman, Coalescents with multiple collisions, Ann. Probab. 27 (4) (1999) 1870-1902. | MR 1742892 | Zbl 0963.60079

[29] D. Ruelle, A mathematical reformulation of Derrida's REM and GREM, Comm. Math. Phys. 108 (1987) 225-239. | MR 875300 | Zbl 0617.60100

[30] J. Smoller, Shock Waves and Reaction-Diffusion Equations, A Series of Comprehensive Studies in Mathematics, vol. 258, Springer, Berlin, 1983. | MR 688146 | Zbl 0508.35002

[31] S. Watanabe, A limit theorem of branching processes and continuous state branching, J. Math. Kyoto University 8 (1968) 141-167. | MR 237008 | Zbl 0159.46201

[32] K. Yosida, Functional Analysis, A Series of Comprehensive Studies in Mathematics, vol. 123, Springer, Berlin, 1971. | MR 500055 | Zbl 0217.16001

[33] V.M. Zolotarev, One-Dimensional Stable Distributions, Translations of Mathematical Monographs, vol. 65, American Mathematical Society, Providence, RI, 1986. | MR 854867 | Zbl 0589.60015