On the Limit Distributions of Some Functionals in Multi-Type Branching Processes

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Next article On the Limit Distributions of Some Functionals in Multi-Type Branching ProcessesI. S. Badalbaev and A. MukhitdinovI. S. Badalbaev and A. Mukhitdinovhttps://doi.org/10.1137/1135095PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. A. Sevast'yanov, Verzweigungsprozesse, Akademie-Verlag, Berlin, 1974xi+326 53:11785 0291.60039 Google Scholar[2] I. S. Badalbaev, A certain estimate for the eigenvalue of the mean value matrix of a branching random process with two types of particles, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1976), 8–13, 83, (In Russian.) 55:4402 Google Scholar[3] I. S. Badalbaev and , A. Mukhitdinov, The role of the spectrum of the eigenvalues of the matrix of mathematical expectations in the limit behavior of the trajectories of a multitype branching process, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1987), 7–12, 77, (In Russian.) 88h:60165 0632.60082 Google Scholar[4] H. Kesten and , B. P. Stigum, Additional limit theorems for indecomposable multidimensional Galton-Watson processes, Ann. Math. Statist., 37 (1966), 1463–1481 34:864 0203.17402 CrossrefGoogle Scholar[5] S. Asmussen and , N. Keiding, Martingale central limit theorems and asymptotic estimation theory for multitype branching processes, Advances in Appl. Probability, 10 (1978), 109–129 57:10769 0391.60076 CrossrefGoogle Scholar[6] Niels Keiding and , Steffen L. Lauritzen, Marginal maximum likelihood estimates and estimation of the offspring mean in a branching process, Scand. J. Statist., 5 (1978), 106–110 81g:62051 0378.62074 Google Scholar[7] Niels Becker, Estimation for discrete time branching processes with application to epidemics, Biometrics, 33 (1977), 515–522 58:31657 0371.92026 CrossrefGoogle Scholar[8] J. P. Dion and , N. Keiding, Statistical inference in branching processesBranching processes (Conf., Saint Hippolyte, Que., 1976), Adv. Probab. Related Topics, Vol. 5, Dekker, New York, 1978, 105–140, Basel 80d:62072 0405.62070 Google Scholar[9] F. R. Gantmacher, The theory of matrices. Vols. 1, 2, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959Vol. 1, x+374 pp. Vol. 2, ix+276 21:6372c Google Scholar[10] William Feller, An introduction to probability theory and its applications. Vol. II, Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 42:5292 0219.60003 Google Scholar[11] I. S. Badalbaev and , A. Mukhitdinov, Limit theorems for some functionals in critical multitype branching processes, Theory Probab. Appl., 34 (1989), 129–133 10.1137/1134004 LinkGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Asymptotic behavior of projections of supercritical multi-type continuous-state and continuous-time branching processes with immigrationAdvances in Applied Probability, Vol. 53, No. 4 | 22 November 2021 Cross Ref Almost sure, L1- and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigrationScience China Mathematics, Vol. 63, No. 10 | 20 April 2020 Cross Ref Identification of multitype branching processesThe Annals of Statistics, Vol. 33, No. 6 | 1 Dec 2005 Cross Ref On Evolution of Random Fields with an Ultra Unbounded Stochastic SourceYu. A. RozanovTheory of Probability & Its Applications, Vol. 38, No. 2 | 28 July 2006AbstractPDF (1246 KB)Statistical inference for branching processes with an increasing random number of ancestorsJournal of Statistical Planning and Inference, Vol. 39, No. 2 | 1 Apr 1994 Cross Ref Volume 35, Issue 4| 1991Theory of Probability & Its Applications625-829 History Submitted:08 October 1987Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135095Article page range:pp. 625-638ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics