Stochastic partial differential equations for a class of interacting measure-valued diffusions

D. A. Dawson; J. Vaillancourt; H. Wang

Annales de l'I.H.P. Probabilités et statistiques (2000)

  • Volume: 36, Issue: 2, page 167-180
  • ISSN: 0246-0203

How to cite

top

Dawson, D. A., Vaillancourt, J., and Wang, H.. "Stochastic partial differential equations for a class of interacting measure-valued diffusions." Annales de l'I.H.P. Probabilités et statistiques 36.2 (2000): 167-180. <http://eudml.org/doc/77655>.

@article{Dawson2000,
author = {Dawson, D. A., Vaillancourt, J., Wang, H.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic partial differential equation; measure-valued processes; cylindrical Brownian motion},
language = {eng},
number = {2},
pages = {167-180},
publisher = {Gauthier-Villars},
title = {Stochastic partial differential equations for a class of interacting measure-valued diffusions},
url = {http://eudml.org/doc/77655},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Dawson, D. A.
AU - Vaillancourt, J.
AU - Wang, H.
TI - Stochastic partial differential equations for a class of interacting measure-valued diffusions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2000
PB - Gauthier-Villars
VL - 36
IS - 2
SP - 167
EP - 180
LA - eng
KW - stochastic partial differential equation; measure-valued processes; cylindrical Brownian motion
UR - http://eudml.org/doc/77655
ER -

References

top
  1. [1] Dawson D.A., Infinitely divisible random measures and superprocesses, in: Proc. 1990 Workshop on Stochastic Analysis and Related Topics, Silivri, Turkey, 1992. Zbl0785.60034MR1203373
  2. [2] Dawson D.A., Vaillancourt J., Stochastic McKean-Vlasov equations, Nonlinear Differential Eq. Appl.2 (1995) 199-229. Zbl0830.60091MR1328577
  3. [3] Dellacherie C., Meyer P.A., Probabilities and Potential B, North-Holland, Amsterdam, 1982. Zbl0494.60002MR745449
  4. [4] Dynkin E.B., Markov Processes, Springer, Berlin, 1965. Zbl0132.37901
  5. [5] Ethier S.N., Kurtz T.G., Markov Processes: Characterization and Convergence, Wiley, New York, 1986. Zbl0592.60049MR838085
  6. [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. Zbl0233.60068MR232439
  7. [7] Jakubowski A., On the Skorohod topology, Ann. Inst. Henri Poincaré22 (3) (1986) 263-285. Zbl0609.60005MR871083
  8. [8] Jakubowski A., Continuity of the Ito stochastic integral in Hilbert spaces, Stochastics59 ( 1996) 169-182. Zbl0868.60047MR1427737
  9. [9] Jakubowski A., The almost sure Skorohod representation for subsequences in nonmetric spaces, Theory Probab. Appl.42 (2) (1997) 167-174. Zbl0923.60001MR1453342
  10. [10] Konno N., Shiga T., Stochastic partial differential equations for some measure-valued diffusions, Probab. Theory Related Fields79 (1988) 201-225. Zbl0631.60058MR958288
  11. [11] Kotelenez P., Existence, uniqueness and smoothness for a class of function valued stochastic partial differential equations, Stochastics41 (1992) 177-199. Zbl0766.60078MR1275582
  12. [12] Kotelenez P., A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid, Ann. Appl. Probab.5 (1995) 1126-1160. Zbl0851.60062MR1384369
  13. [13] Kotelenez P., A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation, Probab. Theory Related Fields102 (1995) 159-188. Zbl0821.60066MR1337250
  14. [14] Mitoma I., Tightness of probabilities on C([0, 1], S') and D([0, 1], S'), Ann. Probab.11 (1983) 989-999. Zbl0527.60004MR714961
  15. [15] Walsh J.B., An introduction to stochastic partial differential equations, in: Lecture Notes in Math., Vol. 1180, 1986, pp. 265-439. Zbl0608.60060MR876085
  16. [16] Wang H., State classification for a class of measure-valued branching diffusions in a Brownian medium, Probab. Theory Related Fields109 (1997) 39-55. Zbl0882.60092MR1469919
  17. [17] Wang H., A class of measure-valued branching diffusions in a random medium, Stochastic Anal. Appl.16 (4) (1998) 753-786. Zbl0913.60091MR1632574

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.