Probabilities of small deviations of a critical Galton-Watson process with infinite variance of the number of the direct descendants of particles
Vladimir VatutinSteklov Mathematical InstituteElena Evgen'evna DyakonovaSteklov Mathematical InstituteYakubdzhan Mukhamadzhanovich KhusanbaevV. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
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We study the asymptotic behaviour of small deviation probabilities for a critical Galton-Watson process with infinite variance of the offspring sizes of particles and apply the result obtained to investigating the structure of a reduced critical Galton-Watson process under the assumption that the original process has a small deviation. Bibliography: 24 titles.
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