Abstract
We establish an asymptotic representation of the maximal eigenvalue ρε for a family of branching processes with arbitrary number of types of particles which are close to critical ones.
References
V. M. Shurenkov, “On the theory of Markov recovery,”Teor. Ver. Primen.,36, No. 2, 248–263 (1984).
V. S. Korolyuk and A. F. Turbin,Mathematical Foundations of the State Lumping of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).
T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1966).
Ya. I. Eleiko, “Transition phenomena for branching processes with arbitrary number of types and with discrete time,”Ukr. Mat. Zh.,34, No. 2, 198–203 (1982).
Additional information
L’viv University, L’viv. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1112–1117, August, 1999.
Rights and permissions
About this article
Cite this article
Eleiko, Y.I. On the asymptotics of the maximal eigenvalue for a family of branching processes. Ukr Math J 51, 1255–1261 (1999). https://doi.org/10.1007/BF02592513
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02592513