Mutually catalytic branching in the plane : uniqueness

Donald A. Dawson; Klaus Fleischmann; Leonid Mytnik; Edwin A. Perkins; Jie Xiong

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 1, page 135-191
  • ISSN: 0246-0203

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Dawson, Donald A., et al. "Mutually catalytic branching in the plane : uniqueness." Annales de l'I.H.P. Probabilités et statistiques 39.1 (2003): 135-191. <http://eudml.org/doc/77754>.

@article{Dawson2003,
author = {Dawson, Donald A., Fleischmann, Klaus, Mytnik, Leonid, Perkins, Edwin A., Xiong, Jie},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {catalytic super-Brownian motion; collision local time; martingale problem duality; uniqueness; Markov property},
language = {eng},
number = {1},
pages = {135-191},
publisher = {Elsevier},
title = {Mutually catalytic branching in the plane : uniqueness},
url = {http://eudml.org/doc/77754},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Dawson, Donald A.
AU - Fleischmann, Klaus
AU - Mytnik, Leonid
AU - Perkins, Edwin A.
AU - Xiong, Jie
TI - Mutually catalytic branching in the plane : uniqueness
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 1
SP - 135
EP - 191
LA - eng
KW - catalytic super-Brownian motion; collision local time; martingale problem duality; uniqueness; Markov property
UR - http://eudml.org/doc/77754
ER -

References

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  1. [1] M. Barlow, S. Evans, E. Perkins, Collision local times and measure-valued processes, Can. J. Math.43 (5) (1991) 897-938. Zbl0765.60044MR1138572
  2. [2] D. Dawson, Measure-valued Markov Processes, École d'été de Probabilités de Saint Flour, 1991. Zbl0799.60080
  3. [3] D. Dawson, A. Etheridge, K. Fleischmann, L. Mytnik, E. Perkins, J. Xiong, Mutually catalytic branching in the plane: Finite measure states, Ann. Probab.30 (4) (2002) 1681-1762. Zbl1017.60098MR1944004
  4. [4] D. Dawson, A. Etheridge, K. Fleischmann, L. Mytnik, E. Perkins, J. Xiong, Mutually catalytic branching in the plane: infinite measure states, Electron. J. Probab.7 (15) (2002). Zbl1016.60075MR1921744
  5. [5] D. Dawson, E. Perkins, Long time behaviour and co-existence in a mutually catalytic branching model, Ann. Probab.26 (3) (1998) 1088-1138. Zbl0938.60042MR1634416
  6. [6] P. Donnelly, T. Kurtz, Particle representations for measure-valued population models, Ann. Probab.27 (1999) 166-205. Zbl0956.60081MR1681126
  7. [7] S.N. Ethier, T.G. Kurtz, Markov Process: Characterization and Convergence, John Wiley and Sons, New York, 1986. Zbl0592.60049MR838085
  8. [8] S. Evans, E. Perkins, Collision local times, historical stochastic calculus, and competing superprocesses, Electron. J. Probab.3 (5) (1998). Zbl0899.60081MR1615329
  9. [9] N. Konno, T. Shiga, Stochastic differential equations for some measure-valued diffusions, Probab. Theory Related Fields79 (1988) 201-225. Zbl0631.60058MR958288
  10. [10] P. Meyer, Un cours sur les intégrales stochastiques, in: Meyer P. (Ed.), Séminaire de Probabilités, X, Lecture Notes in Mathematics, 511, Springer, Berlin, 1976, pp. 245-400. Zbl0374.60070MR501332
  11. [11] L. Mytnik, Superprocesses in random environments, Ann. Probab.24 (1996) 1953-1978. Zbl0874.60041MR1415235
  12. [12] L. Mytnik, Uniqueness for a mutually catalytic branching model, Probab. Theory Related Fields112 (2) (1998) 245-253. Zbl0912.60076MR1653845
  13. [13] E. Perkins, Measure-valued branching diffusions with spatial interactions, Probab. Theory Related Fields94 (1992) 189-245. Zbl0767.60044MR1191108
  14. [14] E. Perkins, On the martingale problem for interactive measure-valued branching diffusions, Mem. Amer. Math. Soc.549 (1995). Zbl0823.60071MR1249422
  15. [15] M. Reimers, One-dimensional stochastic partial differential equations and the branching measure diffusion, Probab. Theory Related Fields81 (1989) 319-340. Zbl0651.60069MR983088
  16. [16] J. Walsh, An introduction to stochastic partial differential equations, Lecture Notes in Mathematics1180 (1986) 265-439. Zbl0608.60060MR876085

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