Extinction for two parabolic stochastic PDE's on the lattice

C. Mueller; E. Perkins

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

  • Volume: 36, Issue: 3, page 301-338
  • ISSN: 0246-0203

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Mueller, C., and Perkins, E.. "Extinction for two parabolic stochastic PDE's on the lattice." Annales de l'I.H.P. Probabilités et statistiques 36.3 (2000): 301-338. <http://eudml.org/doc/77661>.

@article{Mueller2000,
author = {Mueller, C., Perkins, E.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {heat equation; white noise; stochastic partial differential equations; SPDE on the lattice; finite-time extinction},
language = {eng},
number = {3},
pages = {301-338},
publisher = {Gauthier-Villars},
title = {Extinction for two parabolic stochastic PDE's on the lattice},
url = {http://eudml.org/doc/77661},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Mueller, C.
AU - Perkins, E.
TI - Extinction for two parabolic stochastic PDE's on the lattice
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2000
PB - Gauthier-Villars
VL - 36
IS - 3
SP - 301
EP - 338
LA - eng
KW - heat equation; white noise; stochastic partial differential equations; SPDE on the lattice; finite-time extinction
UR - http://eudml.org/doc/77661
ER -

References

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  2. [2] Dawson D.A., Etheridge A., Fleischmann K., Mytnik L., Perkins E., Xiong J., Mutually catalytic super-Brownian motion in R2 (1999), in preparation. 
  3. [3] Dawson D.A., Perkins E., Historical processes, Mem. Amer. Math. Soc.93 (1991). Zbl0754.60062MR1079034
  4. [4] Dawson D.A., Perkins E., Long-time behavior and coexistence in a mutually catalytic branching model, Ann. Probab.26 (3) (1998) 1088-1138. Zbl0938.60042MR1634416
  5. [5] Gärtner J., Molchanov S., Parabolic problems for the Anderson model, Comm. Math. Phys.132 (3) (1990) 613-655. Zbl0711.60055MR1069840
  6. [6] Knight F., Essentials of Brownian Motion and Diffusion, Mathematical Surveys, 18, American Mathematical Society, Providence, RI, 1981. Zbl0458.60002MR613983
  7. [7] Kotelenez P., Comparison methods for a class of function valued stochastic partial differential equations, Probab. Theory Related Fields93 (1) (1992) 1-29. Zbl0767.60053MR1172936
  8. [8] Liggett T.M., Interacting Particle Systems, Springer, Berlin, 1985. Zbl0559.60078MR776231
  9. [9] Mueller C., Perkins E., The compact support property for solutions to the heat equation with noise, Probab. Theory Related Fields93 (1992) 325-358. Zbl0767.60054MR1180704
  10. [10] Mytnik L., Uniqueness for a mutually catalytic branching model, Probab. Theory Related Fields112 (2) (1998) 245-254. Zbl0912.60076MR1653845
  11. [11] Rogers L.C.G., Williams D., Diffusions, Markov Processes, and Martingales, Vol. 2: Ito Calculus, Wiley, Chichester, 1987. Zbl0627.60001MR921238
  12. [12] Walsh J.B., An introduction to stochastic partial differential equations, in: Hennequin PL. (Ed.), Ecole d'Ete de Probabilites de Saint Flour XIV-1984, Lecture Notes in Math., Vol. 1180, Springer, Berlin, 1986. Zbl0608.60060MR876085

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