References
Harris T. E., The Theory of Branching Processes [Russian translation], Mir, Moscow (1966).
Sevast'yanov V. A., Branching Processes [in Russian], Nauka, Moscow (1971).
Lindval T., “On the maximum of a branching process,” Scand. J. Statist. Theory Appl., 3, 209-214 (1976).
Weiner H., “Moments of the maximum in a critical branching process,” J. Appl. Probab., 21, 920-923 (1984).
Borovkov K. A. and Vatutin V. A., “On distribution tails and expectations of maxima in critical branching processes,” J. Appl. Probab., 33, 614-622 (1996).
Vatutin V. A. and Topchiľ V. A., “Maximum of critical Galton-Watson processes and left-continuous random walks,” Teor. Veroyatnost. i Primenen., 42, No. 1,21-34 (1997).
Topchiľ V. A., “Properties of the probability of continuation of general critical branching processes under weak restrictions,” Sibirsk. Mat. Zh., 28, No. 5, 178-192 (1987).
Sze M., “Markov processes associated with critical Galton-Watson processes with application to extinction probabilities,” J. Adv. Appl. Probab., 8, 278-295 (1976).
Resler U., Vatutin V. A., and Topchiľ V. A., “Convergence conditions for branching processes with particles having weigth,” Diskret. Mat., 12, No. 1,9-23 (2000).
Feller W., An Introduction to Probability Theory and Its Applications. Vol. 2 [Russian translation], Mir, Moscow (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bondarenko, E.M., Topchiī, V.A. Estimates for Expectation of the Maximum of a Critical Galton–Watson Process on a Finite Interval. Siberian Mathematical Journal 42, 209–216 (2001). https://doi.org/10.1023/A:1004838911110
Issue Date:
DOI: https://doi.org/10.1023/A:1004838911110