@article{TVP_2014_59_4_a5,
author = {L. Gy\"orfi and M. Isp\'any and P. Kevei and G. Pap},
title = {Asymptotic behavior of multi-type nearly critical {Galton{\textendash}Watson} processes with immigration},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {752--775},
year = {2014},
volume = {59},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2014_59_4_a5/}
}
TY - JOUR AU - L. Györfi AU - M. Ispány AU - P. Kevei AU - G. Pap TI - Asymptotic behavior of multi-type nearly critical Galton–Watson processes with immigration JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2014 SP - 752 EP - 775 VL - 59 IS - 4 UR - http://geodesic.mathdoc.fr/item/TVP_2014_59_4_a5/ LA - en ID - TVP_2014_59_4_a5 ER -
%0 Journal Article %A L. Györfi %A M. Ispány %A P. Kevei %A G. Pap %T Asymptotic behavior of multi-type nearly critical Galton–Watson processes with immigration %J Teoriâ veroâtnostej i ee primeneniâ %D 2014 %P 752-775 %V 59 %N 4 %U http://geodesic.mathdoc.fr/item/TVP_2014_59_4_a5/ %G en %F TVP_2014_59_4_a5
L. Györfi; M. Ispány; P. Kevei; G. Pap. Asymptotic behavior of multi-type nearly critical Galton–Watson processes with immigration. Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 4, pp. 752-775. http://geodesic.mathdoc.fr/item/TVP_2014_59_4_a5/
[1] Altman E., Fiems D., “Branching processes and their generalization applied to wireless networking. Paradigms for Biologically-Inspired Autonomic Networks and Services”, The BIONETS Project e-Book, eds. E. Altman, P. Dini, D. Miorandi, 2012, 54–66
[2] Boon M. A. A., “A polling model with reneging at polling instants”, Ann. Oper. Res., 198 (2012), 5–23 | DOI
[3] Boon M. A. A., Adan I. J. B. F., Boxma O. J., “A polling model with multiple priority levels”, Performance Evaluation, 67 (2010), 468–484 | DOI
[4] Böckenholt U., “Mixed ${{\rm INAR}\,(1)}$ Poisson regression models: Analyzing heterogeneity and serial dependencies in longitudinal count data”, J. Econometrics, 89 (1999), 317–338 | DOI
[5] Doob J. L., Stochastic Processes, Wiley, New York, 1990, 664 pp.
[6] Du J. G., Li Y., “The integer-valued autoregressive (${{\rm INAR}\,(p)}$) model”, J. Time Series Anal., 12:2 (1991), 129–142 | DOI
[7] Franke J., Subba Rao T., Multivariate first order integer valued autoregressions, Technical Report, Mathematics Department, UMIST, Manchester, 1995
[8] Fritz J., “Learning from an ergodic training sequence”, Limit Theorems of Probability Theory, Colloq. (Keszthely, 1974), Colloq. Math. Soc. János Bolyai, 11, North-Holland, Amsterdam, 1975, 79–91
[9] Gladstien K., Lange K., “Equilibrium distributions for deleterious genes in large stationary populations”, Theoret. Population Biol., 14:2 (1978), 322–328 | DOI
[10] Gourieroux C., Jasiak J., “Heterogeneous ${{\rm INAR}(1)}$ model with application to car insurance”, Insurance Math. Econom., 34:2 (2004), 177–192 | DOI
[11] Györfi L., Ispány M., Pap G., Varga K., “Poisson limit of an inhomogeneous nearly critical ${{\rm INAR}(1)}$ model”, Acta Sci. Math. (Szeged), 73:3–4 (2007), 789–815
[12] Johnson N. L., Kotz S., Balakrishnan N., Discrete Multivariate Distributions, John Wiley Sons, New York, 1997, 299 pp.
[13] Haccou P., Jagers P., Vatutin V. A., Branching Processes: Variation, Growth, and Extinction of Populations, Cambridge Univ. Press, Cambridge, 2007, 316 pp.
[14] Kaplan N., “The multitype Galton–Watson process with immigration”, Ann. Probab., 1:6 (1973), 947–953 | DOI
[15] Kevei P., “Asymptotics of nearly critical Galton–Watson process with immigration”, Acta Sci. Math. (Szeged), 77:3–4 (2011), 681–702
[16] Kocherlakota S., Kocherlakota K., Bivariate Discrete Distributions, Dekker, New York, 1992, 361 pp.
[17] Krummenauer F., “Limit theorems for multivariate discrete distributions”, Metrika, 47:1 (1998), 47–69 | DOI
[18] Lange K., Fan R., “Branching process models for mutant genes in nonstationary populations”, Theoret. Population Biol., 51:2 (1997), 118–133 | DOI
[19] van der Mei R. D., “Towards a unifying theory on branching-type polling systems in heavy traffic”, Queueing Syst., 57:1 (2007), 29–46 | DOI
[20] Mode C. J., Multitype Branching Processes. Theory and Applications, Elsevier, New York, 1971, 330
[21] Quine M. P., “The multi-type Galton–Watson process with immigration”, J. Appl. Probab., 7 (1970), 411–422 | DOI
[22] Quine M. P., “The multi-type Galton–Watson process with ${\varrho}$ near to 1”, Adv. Appl. Probab., 4 (1972), 429–452 | DOI
[23] Resing J. A. C., “Polling systems and multitype branching processes”, Queueing Systems, 13:4 (1993), 409–426 | DOI
[24] Weiß Ch. H., “Thinning operations for modeling time series of counts — a survey”, AStA Adv. Statist. Anal., 92:3 (2008), 319–341 | DOI