Large deviation probabilities for some rescaled superprocesses
Fleischmann, Klaus ; Kaj, Ingemar
Annales de l'I.H.P. Probabilités et statistiques, Tome 30 (1994), p. 607-645 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1994-01-01
@article{AIHPB_1994__30_4_607_0,
     author = {Fleischmann, Klaus and Kaj, Ingemar},
     title = {Large deviation probabilities for some rescaled superprocesses},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {30},
     year = {1994},
     pages = {607-645},
     mrnumber = {1302763},
     zbl = {0834.60092},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1994__30_4_607_0}
}

Fleischmann, Klaus; Kaj, Ingemar. Large deviation probabilities for some rescaled superprocesses. Annales de l'I.H.P. Probabilités et statistiques, Tome 30 (1994) pp. 607-645. http://gdmltest.u-ga.fr/item/AIHPB_1994__30_4_607_0/

[1] H. Bauer, Probability Theory and Elements of Measure Theory, 1981, Academic Press, London. | MR 636091 | Zbl 0466.60001

[2] J.T. Cox and D. Griffeath, Occupation times for critical branching Brownian motion, Ann. Probab., 13, 1985, pp. 1108-1132 | MR 806212 | Zbl 0582.60091

[3] D.A. Dawson, Measure-valued Markov Processes, École d'Été de Probabilités de Saint-Flour XXI-1991 (ed. P. L. Hennequin), Lecture Notes Math., Vol. 1541, 1993, pp. 1-260. | MR 1242575 | Zbl 0799.60080

[4] D.A. Dawson and K. Fleischmann, Strong clumping of critical space-time branching models in subcritical dimensions, Stochastic Processes Appl., Vol. 30, 1988, pp. 193-208. | MR 978354 | Zbl 0678.60040

[5] D.A. Dawson and K. Fleischmann, Diffusion and reaction caused by point catalysts, SIAM J. Appl. Math., Vol. 52, 1992, pp. 163-180. | MR 1148324 | Zbl 0781.35026

[6] D.A. Dawson, K. Fleischmann and L.G. Gorostiza, Stable hydrodynamic limit fluctuations of a critical branching particle system in a random medium, Ann. Probab., Vol. 17, 1989, pp. 1083-1117. | MR 1009446 | Zbl 0694.60078

[7] D.A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics, Vol. 20, 1987, pp. 247-308. | MR 885876 | Zbl 0613.60021

[8] A. De Acosta, P. Ney and E. Nummelin, Large deviation lower bounds for general sequences of random variables, In: Random Walks, Brownian Motion and Interacting Particle Systems, A Festschrift in Honor of Frank Spitzer, Editors: R. Durrett and H. Kesten, Progress Probab., Vol. 28, 1991, pp. 215-221, Birkhäuser, Boston. | MR 1146448 | Zbl 0741.60020

[9] J.-D. Deuschel and D.W. Stroock, Large Deviations, 1989, Academic Press, Boston. | MR 997938 | Zbl 0705.60029

[10] R.D. Ellis, Large Deviations for a general class of random vectors, Ann. Probab., Vol. 12, 1984, pp. 1-12. | MR 723726 | Zbl 0534.60026

[11] K. Fleischmann, J. Gärtner and I. Kaj, A Schilder type theorem for super-Brownian motion, Uppsala University, Dept. Math., 1993, Preprint No. 14. | MR 1402327 | Zbl 0860.60066

[12] M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, 1984, Springer-Verlag, New York. | MR 722136 | Zbl 0522.60055

[13] H. Fujita, On the blowing up of solutions of the Cauchy Problem for ut = Δu + u1+α, J. Fac. Sci. Univ. Tokyo, Vol. 13, 1966, pp. 109-124. | MR 214914 | Zbl 0163.34002

[14] I. Iscoe, A weighted occupation time for a class of measure-valued branching processes, Probab. Th. Related Fields, Vol. 71, 1986, pp. 85-116. | MR 814663 | Zbl 0555.60034

[15] I. Iscoe and T.Y. Lee, Large deviations for occupation times of measure-valued branching Brownian motions, Stochastics, Stochastic Reports, Vol. 45, 1993, pp. 177-209. | MR 1306931 | Zbl 0797.60025

[16] O. Kallenberg, Random Measures, 3rd revised and enlarged ed. 1983, Akademie-Verlag, Berlin. | MR 818219 | Zbl 0544.60053

[17] T.Y. Lee, Some limit theorems for super-Brownian motion and semilinear differential equations, Ann. Probab., Vol. 21, 1993, pp. 979-995. | MR 1217576 | Zbl 0776.60038

[18] A. Liemant, Invariante zufällige Punktfolgen, Wiss. Z. Friedrich-Schiller-Universität Jena, Vol. 18, 1969, pp. 361-372. | MR 292151 | Zbl 0265.60082

[19] K. Matthies, J. Kerstan and J. Mecke, Infinitely Divisible Point Processes, 1978, Wiley, Chichester. | MR 517931 | Zbl 0383.60001

[20] C.E. Mueller and F.B. Weissler, Single point blow-up for a general semi-linear heat equation, Indiana Univ. Math. J. Vol. 34, 1985, pp. 881-913. | MR 808833 | Zbl 0597.35057

[21] M. Nagasawa and T. Sirao, Probabilistic treatment of the blowing up of solutions for a nonlinear integral equation, Trans. Amer. Math. Soc., Vol. 139, 1969, pp. 301-310. | MR 239379 | Zbl 0175.40702

[22] E. Zeidler, Nonlinear Functional Analysis and its Applications I, 1986, Springer-Verlag, New York. | MR 816732 | Zbl 0583.47050