The Martin entrance boundary of the Galton–Watson process

Gerold Alsmeyer; Uwe Rösler

Annales de l'I.H.P. Probabilités et statistiques (2006)

  • Volume: 42, Issue: 5, page 591-606
  • ISSN: 0246-0203

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Alsmeyer, Gerold, and Rösler, Uwe. "The Martin entrance boundary of the Galton–Watson process." Annales de l'I.H.P. Probabilités et statistiques 42.5 (2006): 591-606. <http://eudml.org/doc/77910>.

@article{Alsmeyer2006,
author = {Alsmeyer, Gerold, Rösler, Uwe},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Galton–Watson process; quasi-invariant measure; Martin entrance boundary},
language = {eng},
number = {5},
pages = {591-606},
publisher = {Elsevier},
title = {The Martin entrance boundary of the Galton–Watson process},
url = {http://eudml.org/doc/77910},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Alsmeyer, Gerold
AU - Rösler, Uwe
TI - The Martin entrance boundary of the Galton–Watson process
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 5
SP - 591
EP - 606
LA - eng
KW - Galton–Watson process; quasi-invariant measure; Martin entrance boundary
UR - http://eudml.org/doc/77910
ER -

References

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  1. [1] G. Alsmeyer, U. Rösler, Asexual versus promiscuous bisexual Galton–Watson processes: The extinction probability ratio, Ann. Appl. Probab.12 (2002) 125-142. Zbl1020.60073MR1890059
  2. [2] S. Asmussen, H. Hering, Branching Processes, Birkhäuser, Boston, 1983. Zbl0516.60095MR701538
  3. [3] K.B. Athreya, P. Ney, Branching Processes, Springer, New York, 1972. Zbl0259.60002MR373040
  4. [4] T.E. Harris, The Theory of Branching Processes, Springer, Heidelberg, 1963. Zbl0117.13002MR163361
  5. [5] P. Jagers, Branching Processes with Biological Applications, Wiley, London, 1975. Zbl0356.60039MR488341
  6. [6] S. Karlin, J. McGregor, Uniqueness of stationary measures for branching processes and applications, in: Proc. of the Fifth Berkeley Symposium, vol. II, Univ. of California Press, Berkeley, 1967, pp. 243-254. Zbl0218.60074MR214154
  7. [7] J.G. Kemeny, J.L. Snell, A.W. Knapp, Denumerable Markov Chains, Springer, New York, 1976. Zbl0149.13301MR407981
  8. [8] H. Kesten, P. Ney, F. Spitzer, The Galton–Watson process with mean one and finite variance, Theory Probab. Appl.11 (1966) 513-540. Zbl0158.35202MR207052
  9. [9] J.F.C. Kingman, Stationary for branching processes, Proc. Amer. Math. Soc.16 (1965) 245-247. Zbl0132.38305MR173291
  10. [10] F. Papangelou, A lemma on the Galton–Watson process and some of its consequences, Proc. Amer. Math. Soc.19 (1968) 1469-1479. Zbl0174.21301MR232457
  11. [11] E. Seneta, The Galton–Watson process with mean one, J. Appl. Probab.4 (1967) 489-495. Zbl0178.19601MR228075
  12. [12] F. Spitzer, Two explicit Martin boundary constructions, in: Symposium on Probab. Methods in Analysis, Lecture Notes in Math., vol. 31, Springer, Berlin, 1967, pp. 296-298. Zbl0158.12802MR224165

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