Analysis of a Recurrence Related to Critical Nonhomogeneous Branching Processes

REFERENCES

• Bienaymé , J. 1845 . De la loi de multiplication et de la durée des familles . Soc. Philomath. Paris , 5 : 37 – 39 .
   Google Scholar
• Watson , H.W. , and F. Galton . 1874 . On the probability of the extinction of families . J. Anthropol. Inst. Great Britain and Ireland , 4 : 138 – 144 . [CSA]
   Google Scholar
• Kolmogorov , A.N. 1938. On the solution of a biological problem. In Proc. Tomsk University (in Russian) 2:7–12. [CSA]
   Google Scholar
• Kolmogorov , A.N. , and N.A. Dmitriev . 1947 . Branching random processes . Dokl. Acad. Nauk. Proceedings of the Academy of Sciences (in Russian) 56 ( 1 ): 7 – 10 . [CSA]
   Google Scholar
• Kolmogorov , A.N. , and B.A. Sevastyanov . 1947 . The calculation of the final probabilities of branching random processes . Dokl. Acad. Nauk. Proceedings of the Academy of Sciences. (in Russian) 56 ( 8 ): 783 – 786 . [CSA]
   Google Scholar
• Harris , T.E. 1963 . The Theory of Branching Processes . Springer-Verlag .
   Google Scholar
• Sevastyanov , B.A. 1971 . Branching Processes . Nauka ( in Russian ).
   Google Scholar
• Athreya , K. , and P. Ney . 1972 . Branching Processes . Springer-Verlag .
   Google Scholar
• Jagers , P. 1975 . Branching Processes with Biological Applications . Wiley .
   Google Scholar
• Asmussen , S. , and H. Hering . 1983 . Branching Processes . Birkhäuser .
   Google Scholar
• Guttorp , P. 1991 . Statistical Inference for Branching Processes . Wiley .
   Google Scholar
• Yanev , N.M. 1975 . Conditions for degeneracy of ϕ-branching processes with random ϕ . Theory of Probability and Applications 20 : 421 – 428 . [CSA] [CROSSREF]
   Google Scholar
• Sevastyanov , B.A. , and A.M. Zubkov . 1974 . Controlled branching processes . Theory of Probability and Applications 19 : 14 – 24 . [CSA] [CROSSREF]
   Google Scholar
• Yanev , N.M. 1977 . Controlled branching processes in random environment . Math. Balkanica 7 : 137 – 156 . [CSA]
   Google Scholar
• Bruss , F.T. 1980 . A counterpart of the Borel-Cantelli lemma . Journal of Applied Probability 17 : 1094 – 1101 . [CSA]
   Web of Science ®Google Scholar
• González , M. , and M. Molina , and I. del Puerto . 2002 . On the controlled Galton-Watson process with random control function . Journal of Applied Probability 39 : 804 – 815 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• González , M. , and M. Molina , and I. del Puerto . 2003 . On the geometric growth in controlled branching processes with random control function . Journal of Applied Probability 40 : 995 – 1006 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Zubkov , A.M. 1974 . Analogies between Galton-Watson processes and ϕ-branching processes . Theory of Probability and Applications 19 : 309 – 331 . [CSA] [CROSSREF]
   Google Scholar
• Bruss , F.T. 1978 . Branching processes with random absorbing processes . Journal of Applied Probability 15 : 54 – 64 . [CSA]
   Web of Science ®Google Scholar
• Yanev , G.P. , and N.M. Yanev . 1989 . Conditions for extinction of controlled branching processes . In Math. and Educ. in Math. Proc. of the 18th. Spring Conf. of UBM , Sofia : BAS , pp. 550 – 556 .
   Google Scholar
• Yanev , G.P. , and N.M. Yanev . 1990 . Extinction of controlled branching processes in random environments . Math. Balkanica (New Series) 4 : 368 – 380 . [CSA]
   Google Scholar
• Yanev , N.M. , and K.M. Mitov . 1985 . Critical branching processes with nonhomogeneous migration . Annals of Probability 13 ( 3 ): 923 – 933 . [CSA]
   Web of Science ®Google Scholar
• Graham , R.L. , D.E. Knuth , and O. Patashnik . 1994 . Concrete Mathematics, , 2nd ed. , Addison Wesley .
   Google Scholar
• Mitov , K.M. , and N.M. Yanev . 1984 . Critical Galton-Watson processes with decreasing state-dependent immigration . Journal of Applied Probability 21 : 22 – 39 . [CSA]
   Web of Science ®Google Scholar
• Mitov , K.M. , and V.A. Vatutin , and N.M. Yanev . 1984 . Continuous-time branching processes with decreasing state-dependent immigration . Advances in Applied Probability 16 : 697 – 714 . [CSA]
   Web of Science ®Google Scholar
• Bruss , F.T. , and M. Drmota , and G. Louchard . 1998 . The complete solution of the competitive rank selection problem . Algorithmica 22 ( 4 ): 413 – 447 . [CSA]
   Web of Science ®Google Scholar