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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.