Stochastic partial differential equations for a class of interacting measure-valued diffusions
Dawson, D. A. ; Vaillancourt, J. ; Wang, H.
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000), p. 167-180 / Harvested from Numdam
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@article{AIHPB_2000__36_2_167_0,
     author = {Dawson, D. A. and Vaillancourt, J. and Wang, H.},
     title = {Stochastic partial differential equations for a class of interacting measure-valued diffusions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {36},
     year = {2000},
     pages = {167-180},
     mrnumber = {1751657},
     zbl = {0973.60077},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2000__36_2_167_0}
}

Dawson, D. A.; Vaillancourt, J.; Wang, H. Stochastic partial differential equations for a class of interacting measure-valued diffusions. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) pp. 167-180. http://gdmltest.u-ga.fr/item/AIHPB_2000__36_2_167_0/

[1] Dawson D.A., Infinitely divisible random measures and superprocesses, in: Proc. 1990 Workshop on Stochastic Analysis and Related Topics, Silivri, Turkey, 1992. | MR 1203373

[2] Dawson D.A., Vaillancourt J., Stochastic McKean-Vlasov equations, Nonlinear Differential Eq. Appl. 2 (1995) 199-229. | MR 1328577 | Zbl 0830.60091

[3] Dellacherie C., Meyer P.A., Probabilities and Potential B, North-Holland, Amsterdam, 1982. | MR 745449 | Zbl 0494.60002

[4] Dynkin E.B., Markov Processes, Springer, Berlin, 1965. | Zbl 0132.37901

[5] Ethier S.N., Kurtz T.G., Markov Processes: Characterization and Convergence, Wiley, New York, 1986. | MR 838085 | Zbl 0592.60049

[6] Ikeda N., Nagasawa M., Watanabe S., Branching Markov processes, I, II, III, J. Math. Kyoto Univ. 8 (1968) 233-278; 8 (1968) 365-410; 9 (1969) 95-160. | MR 232439 | Zbl 0233.60069 | Zbl 0233.60068

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

[8] Jakubowski A., Continuity of the Ito stochastic integral in Hilbert spaces, Stochastics 59 ( 1996) 169-182. | MR 1427737 | Zbl 0868.60047

[9] Jakubowski A., The almost sure Skorohod representation for subsequences in nonmetric spaces, Theory Probab. Appl. 42 (2) (1997) 167-174. | MR 1453342 | Zbl 0923.60001

[10] Konno N., Shiga T., Stochastic partial differential equations for some measure-valued diffusions, Probab. Theory Related Fields 79 (1988) 201-225. | MR 958288 | Zbl 0631.60058

[11] Kotelenez P., Existence, uniqueness and smoothness for a class of function valued stochastic partial differential equations, Stochastics 41 (1992) 177-199. | MR 1275582 | Zbl 0766.60078

[12] Kotelenez P., A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid, Ann. Appl. Probab. 5 (1995) 1126-1160. | MR 1384369 | Zbl 0851.60062

[13] Kotelenez P., A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation, Probab. Theory Related Fields 102 (1995) 159-188. | MR 1337250 | Zbl 0821.60066

[14] Mitoma I., Tightness of probabilities on C([0, 1], S') and D([0, 1], S'), Ann. Probab. 11 (1983) 989-999. | MR 714961 | Zbl 0527.60004

[15] Walsh J.B., An introduction to stochastic partial differential equations, in: Lecture Notes in Math., Vol. 1180, 1986, pp. 265-439. | MR 876085 | Zbl 0608.60060

[16] Wang H., State classification for a class of measure-valued branching diffusions in a Brownian medium, Probab. Theory Related Fields 109 (1997) 39-55. | MR 1469919 | Zbl 0882.60092

[17] Wang H., A class of measure-valued branching diffusions in a random medium, Stochastic Anal. Appl. 16 (4) (1998) 753-786. | MR 1632574 | Zbl 0913.60091