Branching processes

Handbook of Statistics

Volumn 19, Issue , 2001, Pages 35-53

  Athreya, K B ^a   Vidyashankar, A N ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548058808     PISSN: 01697161     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-7161(01)19004-8     Document Type: Review

References (67)

1. Asmussen S. Convergence rates for branching processes. Ann. Probab. 4 (1976) 139-146
2. Asmussen S. Almost sure behavior of linear functionals of supercritical branching processes. Trans. Amer. Math. Soc. 1 (1977) 233-248
3. Asmussen S. Some martingale methods in the limit theory of supercritical branching processes. Branching Processes. Advances in probability and related topics 5 (1978), Marcel Dekker, Riverside 1-26
4. Asmussen S., and Hering H. Branching Processes (1983), Birkhauser, New York
5. Asmussen S., and Kaplan N. Branching Random walks I. Stoch. proc. Appl. 4 1 (1976) 1-13
6. Asmussen S., and Kaplan N. Branching Random walks II. Stoch. proc. Appl. 4 1 (1976) 15-31
7. Asmussen S., and Keiding N. Martingale central limit theorems and asymptotic estimation theory for multitype branching processes. Adv. Appl. Probab. 10 1 (1978) 109-129
8. Asmussen S., and Kurtz T. Necessary and sufficient conditions for complete convergence in the law of large numbers. Ann. Probab. 8 1 (1980) 176-182
9. Athreya K.B. Some results on multitype continuous time Markov branching processes. Ann. Math. Statist. 20 (1968) 649-651
10. Athreya K.B. Limit theorems for multitype continuous time Markov branching processes II - the case of an arbitrary linear functional. Z. Wahrsc. Verw. Gebiete 13 (1969) 204-214
11. Athreya K.B. On the absolute continuity of the limit random variable in the supercritical Galton-Watson branching processes. Proc. Amer. Math. Soc. 30 (1971) 563-565
12. Athreya K.B. A simple proof of a result of Kesten and Stigum on supercritical multitype Galton-Watson branching process. Ann. Math. Statist. 41 (1970) 195-202
13. Athreya K.B. Discounted branching random walks. Adv. Appl. Probab. 17 1 (1985) 53-66
14. Athreya K.B. Large deviation rates for branching processes-1, the single type case. Ann. Appl. Probab. 4 3 (1994) 779-790
15. Preprint M99-12. Athreya K.B. Growth rates of lines of descent in branching process may differ (1999), Department of Mathematics, Boston
16. Athreya K.B., and Jagers P. Classical and modern branching processes. Papers from IMA workshop held at the University of Minnesota. Minneapolis, MN, June 13-17, 1994. IMA volumes in Mathematics and Applications 84 (1997), Springer-Verlag, Iowa State University
17. Athreya K.B., and Kang H. Some limit theorems for positive recurrent branching Markov chains, I. Adv. Appl. Probab. 30 (1998) 693-710
18. Athreya K.B., and Kang H. Some limit theorems for positive recurrent branching Markov chains, II. Adv. Appl. Probab. 30 (1998) 711-722
19. Athreya K.B., and Kaplan N. Convergence of age distribution in the one-dimensional supercritical age dependent branching process. Ann. Probab. 42 1 (1976) 38-50
20. Athreya K.B., and Karlin S. On branching processes with random environments, I - Extinction Probabilities. Ann. Math. Statist. 42 (1971) 1499-1520
21. Athreya K.B., and Karlin S. On branching processes with random environments, II - Limit Theorems. Ann. Math. Statist. 42 (1971) 1843-1858
22. Athreya K.B., and Ney P. The local limit theorem and some related aspects of supercritical branching processes. Trans. Amer. Math. 152 (1970) 233-251
23. Athreya K.B., and Ney P. Branching Processes (1972), Springer-Verlag, New York
24. Athreya K.B., and Vidyashankar A.N. Large deviation results for branching processes, Stochastic Processes. A Fetschrift in honour of G. Kallianpur (1993), Springer, New York 7-12
25. Athreya K.B., and Vidyashankar A.N. Large deviation rates for branching processes II - the multitype case. Ann. Appl. Probab. 5 2 (1995) 566-576
26. Athreya K.B., and Vidyashankar A.N. Large deviation rates for critical and supercritical branching processes. Classical and Modern Branching Processes. IMA volumes in Mathematics and its Applications Vol. 84 (1997), Springer, New York 1-18
27. Biggins J.D. Chernoff's theorem in the branching random walk. J. Appl. Probab. 14 3 (1977) 630-636
28. Biggins J.D. Martingale convergence in the branching random walk. J. Appl. Probab. 1 (1977) 25-37
29. Biggins J.D. Growth rates in the branching random walk. Z. Wahrsch. Verw. Gebiete 48 1 (1979) 17-34
30. Biggins J.D. Uniform convergence of martingales in the branching random walk. Ann. Probab. 20 1 (1992) 137-151
31. Biggins J.D., and Kyprianou A.E. A Seneta-Heyde norming in the branching random walk. Ann. Probab. 25 1 (1997) 337-360
32. Bramson M., Ney P., and Tao J. The population composition of a multitype branching random walk. Ann. Appl. Probab. 3 (1992) 575-596
33. Cohn H. On the growth of multitype supercritical branching processes in a random environment. Ann. Probab. 17 3 (1989) 1118-1123
34. Dawson D.A. Measure-valued Markov Processes École d'Été de Probabilitiés de Saint-Flour XXI. Lecture Notes in Mathematics 1541 (1991), Springer-Verlag, New York
35. Dion J.-P., and Essebbar B. On the statistics of controlled branching processes. Branching Processes. Lecture Notes in Statistics 99 (1993), Springer, Berlin 14-21
36. Datta S., and Sriram T.N. A modified bootstrap for branching processes with immigration. Stoch. Proc. Appl. 56 2 (1995) 275-294
37. Goldstein M.I. Critical age-dependent branching processes-Single and Multitype. Z. Wahrsch. Verw. Gebiete 17 (1971) 74-88
38. Grey D.R. On regular branching processes with infinite mean. Stoch. Proc. Appl. 8 (1979) 257-267
39. Grey D.R. A new look at convergence of branching processes. Ann. Probab. 8 (1980) 377-380
40. Guttorp P. Statistical Inference for Branching Processes (1991), John Wiley and Sons, New York
41. Harris T.E. The Theory of Branching Processes (1963), Springer, New York
42. Heyde C.C. Extension of a result of Seneta for supercritical Galton-Watson Processes. Ann. Math. Statist. 41 (1970) 739-742
43. Heyde C.C. Some central-limit analogues for supercritical branching processes. J. Appl. Probab. 8 (1971) 52-59
44. Heyde C.C. Some almost sure convergence theorems for supercritical branching processes. Z. Wahrsc. Verw. Gebiete 20 (1971) 189-192
45. Hoppe F.M. Supercritical multitype branching processes. Ann. Probab. 4 3 (1976) 393-401
46. Jagers P. Branching processes with biological applications (1975), Wiley Interscience, Berlin
47. Jagers P. The growth and stabilization of populations. Statist. Sci. 6 3 (1991) 269-283
48. Joffe A. A new martingale in the branching random walk. Ann. Appl. Probab. 3 4 (1993) 1145-1150
49. Joffe A., and Spitzer F. On multitype branching processes with ρ ≤ 1. J. Math. Anal. Appl. 19 (1967) 409-430
50. Kesten H., and Stigum B.P. A limit theorem for multidimensional Galton-Watson processes. Ann. Math. Statist. 37 (1966) 1211-1223
51. Kurtz T., Lyons R., Pemantle R., and Peres Y. A conceptual proof of Kesten-Stigum theorem for multi-type branching processes. Classical and Modern Branching Processes. IMA Volumes in Mathematics and its Applications Vol. 84 (1997), Springer, New York 181-186
52. Lyons R., Pemantle R., and Peres Y. Conceptual proofs of LlogL criteria for mean behavior of branching processes. Ann. Probab. 23 (1995) 1125-1138
53. Lyons R. A simple path to Biggins' martingale convergence for branching random walk. 217-222. Classical and Modern Branching Processes. IMA Volumes in Mathematics and its Applications Vol. 84 (1997), Springer, New York 181-186
54. Mode C.J. Multitype branching processes: Theory and applications (1971), American Elsevier Publishing Co. Inc, New York
55. Ney P. The convergence of a random distribution associated with branching process. J. Math. Anal. Appl. 12 (1966) 316-327
56. Ryan Jr. T.A. A multidimensional renewal theorem. Ann. Probab. 4 (1976) 661-665
57. Schuh H.-J., and Barbour A.D. On asymptotic behaviour of branching processes with infinite mean. Adv. Appl. Probab. 9 (1977) 681-723
58. Schuh H.-J. Seneta constants for the supercritical Bellman Harris process. Adv. Appl. Probab. 14 (1982) 732-751
59. Seneta E. The Galton-Watson process with mean one. J. Appl. Probab. 4 (1967) 489-495
60. Seneta E. On recent theorems concerning supercritical Galton-Watson processes. Ann. Math. Statist. 39 (1968) 2098-2102
61. Seneta E., and Heyde C.C. I.G. Bienayme: Statistical Theory anticipated (1977), Springer-Verlag, New York
62. Sriram T.N., Basawa I.V., and Huggins R.M. Sequential estimation for branching processes with immigration. Ann. Statist. 19 4 (1991) 2232-2243
63. Sun F., and Waterman M.S. Whole genome amplification and branching processes. Adv. Appl. Probab. 29 3 (1997) 629-688
64. Tanny D. Limit theorems for branching processes in random environment. Ann. Probab. 5 1 (1977) 100-116
65. Vidyashankar A.N. Large deviations for branching processes in fixed and random environments. Ph.D. Thesis (1994), Departments of Mathematics and Statistics, Iowa State University, New York
66. Wei C.Z., and Winnicki J. Estimation of means in the branching process with immigration. Ann. Statist. 18 4 (1990) 1757-1773
67. Winnicki J. Estimation of variances in the branching process with immigration. Probab. Theory Relat. Fields 88 1 (1991) 77-106