Law of large numbers for superdiffusions : the non-ergodic case

János Engländer

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 1, page 1-6
  • ISSN: 0246-0203

Abstract

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In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. Inter alia, we prove the analog of the Watanabe–Biggins LLN for super-brownian motion.

How to cite

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Engländer, János. "Law of large numbers for superdiffusions : the non-ergodic case." Annales de l'I.H.P. Probabilités et statistiques 45.1 (2009): 1-6. <http://eudml.org/doc/78015>.

@article{Engländer2009,
abstract = {In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. Inter alia, we prove the analog of the Watanabe–Biggins LLN for super-brownian motion.},
author = {Engländer, János},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {super-brownian motion; superdiffusion; superprocess; law of large numbers; H-transform; weighted superprocess; scaling limit; local extinction; super-Brownian motion},
language = {eng},
number = {1},
pages = {1-6},
publisher = {Gauthier-Villars},
title = {Law of large numbers for superdiffusions : the non-ergodic case},
url = {http://eudml.org/doc/78015},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Engländer, János
TI - Law of large numbers for superdiffusions : the non-ergodic case
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 1
SP - 1
EP - 6
AB - In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. Inter alia, we prove the analog of the Watanabe–Biggins LLN for super-brownian motion.
LA - eng
KW - super-brownian motion; superdiffusion; superprocess; law of large numbers; H-transform; weighted superprocess; scaling limit; local extinction; super-Brownian motion
UR - http://eudml.org/doc/78015
ER -

References

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  1. [1] J. D. Biggins. Uniform convergence of martingales in the branching random walk. Ann. Probab. 20 (1992) 137–151. Zbl0748.60080MR1143415
  2. [2] J. Engländer and R. G. Pinsky. On the construction and support properties of measure-valued diffusions on D⊂ℝd with spatially dependent branching. Ann. Probab. 27 (1999) 684–730. Zbl0979.60078MR1698955
  3. [3] J. Engländer and R. G. Pinsky. The compact support property for measure-valued processes. Ann. Inst. H. Poincaré Probab. Statist. 42 (2006) 535–552. Zbl1104.60049MR2259973
  4. [4] J. Engländer and D. Turaev. A scaling limit theorem for a class of superdiffusions. Ann. Probab. 30 (2002) 683–722. Zbl1014.60080MR1905855
  5. [5] J. Engländer and A. Winter. Law of large numbers for a class of superdiffusions. Ann. Inst. H. Poincaré Probab. Statist. 42 (2006) 171–185. Zbl1093.60058MR2199796
  6. [6] R. G. Pinsky. On the large time growth rate of the support of supercritical super-Brownian motion. Ann. Probab. 23 (1995) 1748–1754. Zbl0852.60094MR1379166
  7. [7] S. Watanabe. Limit theorems for a class of branching processes. In Markov Processes and Potential Theory 205–232. J. Chover, Ed. Wiley, New York, 1967. Zbl0253.60072MR237007

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