On long time almost sure asymptotics of renormalized branching diffusion processes

Nicolas Fournier; Bernard Roynette

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

  • Volume: 39, Issue: 6, page 979-991
  • ISSN: 0246-0203

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Fournier, Nicolas, and Roynette, Bernard. "On long time almost sure asymptotics of renormalized branching diffusion processes." Annales de l'I.H.P. Probabilités et statistiques 39.6 (2003): 979-991. <http://eudml.org/doc/77792>.

@article{Fournier2003,
author = {Fournier, Nicolas, Roynette, Bernard},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Branching diffusion processes; Long time behaviour},
language = {eng},
number = {6},
pages = {979-991},
publisher = {Elsevier},
title = {On long time almost sure asymptotics of renormalized branching diffusion processes},
url = {http://eudml.org/doc/77792},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Fournier, Nicolas
AU - Roynette, Bernard
TI - On long time almost sure asymptotics of renormalized branching diffusion processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 6
SP - 979
EP - 991
LA - eng
KW - Branching diffusion processes; Long time behaviour
UR - http://eudml.org/doc/77792
ER -

References

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  1. [1] N. Dunford, J. Schwartz, Linear Operators, Part II, Spectral Theory, Selfadjoint Operators in Hilbert Space, Reprint of the 1963 original, Wiley Classics Library, 1988. Zbl0128.34803MR1009163
  2. [2] E.B. Dynkin, Branching particle systems and superprocesses, Ann. Probab.19 (3) (1991) 1157-1194. Zbl0732.60092MR1112411
  3. [3] J. Engländer, D. Turaev, A scaling limit theorem for a class of superdiffusions, Ann. Probab.30 (2) (2002) 683-722. Zbl1014.60080MR1905855
  4. [4] C. Fefferman, A. Sanchez-Calle, Fundamental solutions for second order subelliptic operators, Ann. of Math.124 (1986) 247-272. Zbl0613.35002MR855295
  5. [5] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1989. Zbl0684.60040MR1011252
  6. [6] H. Kesten, B. Stigum, A limit theorem for multidimensional Galton–Watson processes, Ann. Math. Statist.37 (1966) 1211-1223. Zbl0203.17401
  7. [7] T. Kurtz, R. Lyons, R. Pemantle, Y. Peres, A conceptual proof of the Kesten–Stigum theorem for multi-type branching processes, in: Athreya K., Jagers P. (Eds.), Classical and Modern Branching Processes (Minneapolis, 1994), IMA Vol. Math. Appl., 84, Springer, New York, 1997, pp. 181-185. Zbl0868.60068
  8. [8] R.G. Pinsky, Transience, reccurence and local extinction properties of the support for supercritical finite measure-valued diffusions, Ann. Probab.24 (1) (1996) 237-267. Zbl0854.60087MR1387634

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