The compact support property for measure-valued processes

Engländer, János; Pinsky, Ross G.

Engländer, János ; Pinsky, Ross G.

Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006), p. 535-552 / Harvested from Numdam

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Publié le : 2006-01-01

MR 2259973 | Zbl 1104.60049 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.anihpb.2005.07.001

@article{AIHPB_2006__42_5_535_0,
     author = {Engl\"ander, J\'anos and Pinsky, Ross},
     title = {The compact support property for measure-valued processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {42},
     year = {2006},
     pages = {535-552},
     doi = {10.1016/j.anihpb.2005.07.001},
     mrnumber = {2259973},
     zbl = {1104.60049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2006__42_5_535_0}
}

Engländer, János; Pinsky, Ross G. The compact support property for measure-valued processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) pp. 535-552. doi : 10.1016/j.anihpb.2005.07.001. http://gdmltest.u-ga.fr/item/AIHPB_2006__42_5_535_0/

Bibliographie

[1] P. Baras, M. Pierre, Problèmes paraboliques semi-linéaires avec données mesures, Appl. Anal. 18 (1984) 111-149. | MR 762868 | Zbl 0582.35060

[2] H. Brezis, L. Veron, Removable singularities for some nonlinear elliptic equations, Arch. Rational Mech. Anal. 75 (1980) 1-6. | MR 592099 | Zbl 0459.35032

[3] 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. | Zbl 0799.60080

[4] D.A. Dawson, I. Iscoe, E.A. Perkins, Super-Brownian motion: path properties and hitting probabilities, Probab. Theory Related Fields 83 (1989) 135-205. | MR 1012498 | Zbl 0692.60063

[5] R.D. Deblassie, On hitting single points by a multidimensional diffusion, Stochastics Stochastics Rep. 65 (1998) 1-11. | MR 1708432 | Zbl 0916.60066

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

[7] E.B. Dynkin, Superprocesses and partial differential equations, Ann. Probab. 21 (1993) 1185-1262. | MR 1235414 | Zbl 0806.60066

[8] S. Dynkin, E.B. Kuznetsov, Superdiffusions and removable singularities for quasilinear partial differential equations, Comm. Pure Appl. Math. 49 (1996) 125-176. | MR 1371926 | Zbl 0861.60083

[9] J. Engländer, Criteria for the existence of positive solutions to the equation $ρ Δ u = u^{2}$ in $R^{d}$ for all $d \geq 1$ - a new probabilistic approach, Positivity 4 (2000) 327-337. | Zbl 0962.35048

[10] J. Engländer, R. Pinsky, On the construction and support properties of measure-valued diffusions on $D \subset R^{d}$ with spatially dependent branching, Ann. Probab. 27 (1999) 684-730. | Zbl 0979.60078

[11] J. Englan̈Der, R. Pinsky, Uniqueness/nonuniqueness for nonnegative solutions of second-order parabolic equations of the form $u_{t} = L u + V u - γ u^{p}$ in $R^{n}$ , J. Differential Equations 192 (2003) 396-428. | Zbl 1081.35050

[12] K. Fleischmann, A. Sturm, A super-stable motion with infinite mean branching, Ann. Inst. H. Poincaré Probab. Statist. 40 (2004) 513-537. | Numdam | MR 2086012 | Zbl 1052.60065

[13] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. | MR 710486 | Zbl 0516.47023

[14] R. Pinsky, Positive Harmonic Functions and Diffusion, Cambridge University Press, 1995. | MR 1326606 | Zbl 0858.31001

[15] R. Pinsky, Positive solutions of reaction diffusion equations with super-linear absorption: universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions, J. Differential Equations, in press. | MR 2183378 | Zbl 1087.35047

[16] Y. Ren, Support properties of super-Brownian motions with spatially dependent branching rate, Stochastic Process. Appl. 110 (2004) 19-44. | MR 2052135 | Zbl 1075.60114

[17] L. Veron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal. 5 (1981) 225-242. | MR 607806 | Zbl 0457.35031