Minimal moment conditions in the limit theory for general Markov branching processes

H. Hering

Annales de l'I.H.P. Probabilités et statistiques (1977)

  • Volume: 13, Issue: 4, page 299-319
  • ISSN: 0246-0203

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Hering, H.. "Minimal moment conditions in the limit theory for general Markov branching processes." Annales de l'I.H.P. Probabilités et statistiques 13.4 (1977): 299-319. <http://eudml.org/doc/77070>.

@article{Hering1977,
author = {Hering, H.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Indecomposable Branching Processes; Galton-Watson Processes; Branching Diffusions},
language = {eng},
number = {4},
pages = {299-319},
publisher = {Gauthier-Villars},
title = {Minimal moment conditions in the limit theory for general Markov branching processes},
url = {http://eudml.org/doc/77070},
volume = {13},
year = {1977},
}

TY - JOUR
AU - Hering, H.
TI - Minimal moment conditions in the limit theory for general Markov branching processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1977
PB - Gauthier-Villars
VL - 13
IS - 4
SP - 299
EP - 319
LA - eng
KW - Indecomposable Branching Processes; Galton-Watson Processes; Branching Diffusions
UR - http://eudml.org/doc/77070
ER -

References

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  1. [0] M.G. Krein and M.A. Rutman, Linear operators leaving invariant a cone in a Banach space. Uspeki Matem. Nauk, t. 3, 1948, p. 1-95; Amer. Math. Soc. Translat., (1), t. 26, 1950. Zbl0030.12902MR38008
  2. [1] T.E. Harris, The Theory of Branching Processes. Springer-Verlag, Berlin-Göttingen- Heidelberg, 1963. Zbl0117.13002MR163361
  3. [2] A. Joffe and F. Spitzer, On multitype branching processes with ρ ≤ 1. J. Math. Anal. Appl., t. 19, 1967, p. 409-430. Zbl0178.19504MR212895
  4. [3] N. Ikeda, M. Nagasawa and S. Watanabe, Branching Markov processes I, II, III. J. Math. Kyoto Univ., t. 8, 1968, p. 233-278, 365-410; t. 9, 1969, p. 95-160. Zbl0233.60068MR232439
  5. [4] T. Savits, The explosion problem for branching Markov process. Osaka J. Math., t. 6, 1969, p. 375-395. Zbl0216.47104MR282426
  6. [5] K.B. Athreya, On the supercritical one dimensional age dependent branching processes. Ann. Math. Statist., t. 40, 1969, p. 743-763. Zbl0175.46603MR243628
  7. [6] H. Hering, Limit theorem for critical branching diffusion processes with absorbing barriers. Math. Biosci., t. 19, 1974, p. 355-370. Zbl0282.60053MR341641
  8. [7] S. Asmussen and H. Hering, Strong limit theorems for general supercritical branching processes with applications to branching diffusions. Z. Wahrscheinlichkeitsth. verw. Geb., t. 36, 1976, p. 195-212. Zbl0325.60081MR420889
  9. [8] S. Asmussen and H. Hering, Strong limit theorems for supercritical immigration branching processes. Math. Scand., t. 39, 1976, p. 327-342. Zbl0348.60117MR438498
  10. [9 a] H. Hering, Refined positivity theorem for semigroups generated by perturbed differential operators of second order with an application to Markov branching processes. Math. Proc. Cambr. Phil. Soc., t. 83, 1976. Zbl0374.47020MR467043
  11. [9 b] H. Hering, Uniform primitivity of semigroups generated by perturbed elliptic differential operators. Math. Proc. Cambr. Phil. Soc., t. 83, 1976. Zbl0374.47021MR467044
  12. [10] H. Hering, Subcritical branching diffusions. Compositio Math., t. 34, 1977, p. 289- 306. Zbl0368.60093MR438501
  13. [11] S. Asmussen and H. Hering, Some modified branching diffusion models. Math. Biosci., t. 34, 1977. Zbl0369.60103MR682242

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