메뉴 건너뛰기




Volumn 109, Issue 1, 2004, Pages 113-144

On weighted branching processes in random environment

Author keywords

Stationary ergodic random environment; Weighted branching process

Indexed keywords


EID: 0242467547     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2003.09.004     Document Type: Article
Times cited : (23)

References (42)
  • 1
    • 0002630691 scopus 로고
    • On the extinction times of varying and random environment branching process
    • Agresti A. On the extinction times of varying and random environment branching process J. Appl. Probab. 12 1975 39-46
    • (1975) J. Appl. Probab. , vol.12 , pp. 39-46
    • Agresti, A.1
  • 3
    • 0000546035 scopus 로고
    • Branching processes with random environments, I: Extinction probabilities
    • Athreya K.B. Karlin S. Branching processes with random environments, I: extinction probabilities Ann. Math. Statist. 42 1971 1499-1520
    • (1971) Ann. Math. Statist. , vol.42 , pp. 1499-1520
    • Athreya, K.B.1    Karlin, S.2
  • 4
    • 0011355047 scopus 로고
    • Branching processes with random environments, II: Limit theorems
    • Athreya K.B. Karlin S. Branching processes with random environments, II: limit theorems Ann. Math. Statist. 42 1971 1843-1858
    • (1971) Ann. Math. Statist. , vol.42 , pp. 1843-1858
    • Athreya, K.B.1    Karlin, S.2
  • 6
    • 0002244969 scopus 로고
    • Martingale convergence in the branching random walk
    • Biggins J.D. Martingale convergence in the branching random walk J. Appl. Probab. 14 1977 25-37
    • (1977) J. Appl. Probab. , vol.14 , pp. 25-37
    • Biggins, J.D.1
  • 7
    • 0001797325 scopus 로고
    • Growth rates in the branching random walk
    • Biggins J.D. Growth rates in the branching random walk Z. Wahrsch. Verw. Geb. 48 1979 17-34
    • (1979) Z. Wahrsch. Verw. Geb. , vol.48 , pp. 17-34
    • Biggins, J.D.1
  • 8
    • 0001837271 scopus 로고
    • Uniform convergence of martingales in the branching random walk
    • Biggins J.D. Uniform convergence of martingales in the branching random walk Ann. Probab. 20 1992 137-151
    • (1992) Ann. Probab. , vol.20 , pp. 137-151
    • Biggins, J.D.1
  • 9
    • 0018752527 scopus 로고
    • Continuity of limit variables in the branching random walk
    • Biggins J.D. Grey D.R. Continuity of limit variables in the branching random walk J. Appl. Probab. 16 1979 740-749
    • (1979) J. Appl. Probab. , vol.16 , pp. 740-749
    • Biggins, J.D.1    Grey, D.R.2
  • 10
    • 0031496422 scopus 로고    scopus 로고
    • Seneta-Heyde norming in the branching random walk
    • Biggins J.D. Kyprianou A.E. Seneta-Heyde norming in the branching random walk Ann. Probab. 25 1997 337-360
    • (1997) Ann. Probab. , vol.25 , pp. 337-360
    • Biggins, J.D.1    Kyprianou, A.E.2
  • 11
    • 0004256573 scopus 로고
    • Reading, MA: Addison-Wesley
    • Breiman L. Probability 1968 Addison-Wesley Reading, MA
    • (1968) Probability
    • Breiman, L.1
  • 13
    • 0040685424 scopus 로고
    • Arbres et processus de Bellman-Harris
    • Chauvin B. Arbres et processus de Bellman-Harris Ann. Inst. H. Poincaré 22 1986 209-232
    • (1986) Ann. Inst. H. Poincaré , vol.22 , pp. 209-232
    • Chauvin, B.1
  • 14
    • 0242641702 scopus 로고
    • A necessary and sufficient condition for noncertain extinction of a branching process in a random environment
    • Coffey J. Tanny D. A necessary and sufficient condition for noncertain extinction of a branching process in a random environment Stochastic Process. Appl. 16 1984 189-197
    • (1984) Stochastic Process. Appl. , vol.16 , pp. 189-197
    • Coffey, J.1    Tanny, D.2
  • 15
    • 38249036800 scopus 로고
    • On the survival probability of a branching process in a finite state i.i.d. environment
    • Dekking F.M. On the survival probability of a branching process in a finite state i.i.d. environment Stochastic Process. Appl. 27 1987 151-157
    • (1987) Stochastic Process. Appl. , vol.27 , pp. 151-157
    • Dekking, F.M.1
  • 17
    • 0034563393 scopus 로고    scopus 로고
    • The survival probability of a critical branching process in a random environment
    • Geiger J. Kersting G. The survival probability of a critical branching process in a random environment Theory Probab. Appl. 45 2000 517-525
    • (2000) Theory Probab. Appl. , vol.45 , pp. 517-525
    • Geiger, J.1    Kersting, G.2
  • 18
    • 0038243162 scopus 로고    scopus 로고
    • Limit theorems for subcritical branching processes in random environment
    • Geiger J. Kersting G. Vatutin V.A. Limit theorems for subcritical branching processes in random environment Ann. Inst. H. Poincaré 39 2003 593-620
    • (2003) Ann. Inst. H. Poincaré , vol.39 , pp. 593-620
    • Geiger, J.1    Kersting, G.2    Vatutin, V.A.3
  • 19
    • 0003322695 scopus 로고
    • The exact Hausdorff dimension in random recursive constructions
    • Graf S. Mauldin R.D. Williams S.C. 1988 The exact Hausdorff dimension in random recursive constructions. Mem. Amer. Math. Soc. 71 381 121 pp.
    • (1988) Mem. Amer. Math. Soc. , vol.71 , Issue.381 , pp. 121
    • Graf, S.1    Mauldin, R.D.2    Williams, S.C.3
  • 20
    • 0039180989 scopus 로고
    • Almost sure convergence of branching processes in varying and random environments
    • Lindvall T. Almost sure convergence of branching processes in varying and random environments Ann. Probab. 2 1974 344-346
    • (1974) Ann. Probab. , vol.2 , pp. 344-346
    • Lindvall, T.1
  • 21
    • 3342908453 scopus 로고    scopus 로고
    • Sur une équation fonctionelle et ses applications: Une extension du théorème de Kesten-Stigum concernant des processus de branchement
    • Liu Q. Sur une équation fonctionelle et ses applications: une extension du théorème de Kesten-Stigum concernant des processus de branchement Adv. Appl. Probab. 29 1997 353-373
    • (1997) Adv. Appl. Probab. , vol.29 , pp. 353-373
    • Liu, Q.1
  • 22
    • 0032025081 scopus 로고    scopus 로고
    • Fixed points of a generalized smoothing transform and applications to the branching random walk
    • Liu Q. Fixed points of a generalized smoothing transform and applications to the branching random walk Adv. Appl. Probab. 30 1998 85-112
    • (1998) Adv. Appl. Probab. , vol.30 , pp. 85-112
    • Liu, Q.1
  • 23
    • 0002649784 scopus 로고    scopus 로고
    • Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks
    • Liu Q. Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks Stochastic Process. Appl. 82 1999 61-87
    • (1999) Stochastic Process. Appl. , vol.82 , pp. 61-87
    • Liu, Q.1
  • 24
    • 0001019904 scopus 로고    scopus 로고
    • On generalized multiplicative cascades
    • Liu Q. On generalized multiplicative cascades Stochastic Process. Appl. 86 2000 263-286
    • (2000) Stochastic Process. Appl. , vol.86 , pp. 263-286
    • Liu, Q.1
  • 25
    • 0008984822 scopus 로고    scopus 로고
    • A simple path to Biggins' martingale convergence for branching random walk
    • Athreya, K.B., Jagers, P. (Eds.), IMA Vol. Mathematical Application Springer, New York
    • Lyons R. 1997 A simple path to Biggins' martingale convergence for branching random walk. In: Athreya, K.B., Jagers, P. (Eds.), Classical and Modern Branching Processes, IMA Vol. Mathematical Application, Vol. 84. Springer, New York, pp. 217-221.
    • (1997) Classical and Modern Branching Processes , vol.84 , pp. 217-221
    • Lyons, R.1
  • 26
    • 0000028988 scopus 로고
    • Conceptual proofs of L log L criteria for mean behavior of branching processes
    • Lyons R. Pemantle R. Peres Y. Conceptual proofs of L log L criteria for mean behavior of branching processes Ann. Probab. 25 1995 1125-1138
    • (1995) Ann. Probab. , vol.25 , pp. 1125-1138
    • Lyons, R.1    Pemantle, R.2    Peres, Y.3
  • 27
    • 0006799223 scopus 로고
    • Random recursive constructions: Asymptotic geometric and topological properties
    • Mauldin R.D. Williams S.C. Random recursive constructions: asymptotic geometric and topological properties Trans. Amer. Math. Soc. 295 1986 325-346
    • (1986) Trans. Amer. Math. Soc. , vol.295 , pp. 325-346
    • Mauldin, R.D.1    Williams, S.C.2
  • 28
    • 0000458044 scopus 로고
    • Arbres et processus de Galton-Watson
    • Neveu J. Arbres et processus de Galton-Watson Ann. Inst. H. Poincaré 22 1986 199-207
    • (1986) Ann. Inst. H. Poincaré , vol.22 , pp. 199-207
    • Neveu, J.1
  • 29
    • 0013238280 scopus 로고
    • The occurrence of large values in stationary sequences
    • O'Brien G.L. The occurrence of large values in stationary sequences Z. Wahrsch. Verw. Gebiete 61 1982 347-353
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.61 , pp. 347-353
    • O'Brien, G.L.1
  • 30
  • 31
    • 38249008257 scopus 로고
    • A fixed point theorem for distributions
    • Rösler U. A fixed point theorem for distributions Stoch. Proc. Appl. 42 1992 195-214
    • (1992) Stoch. Proc. Appl. , vol.42 , pp. 195-214
    • Rösler, U.1
  • 32
    • 29444435685 scopus 로고
    • The weighted branching process
    • Technical Report, University of Kiel
    • Rösler U. 1993 The weighted branching process. Technical Report, University of Kiel.
    • (1993)
    • Rösler, U.1
  • 33
    • 26744474377 scopus 로고    scopus 로고
    • The X ln X condition for the weighted branching process
    • Technical Report, University of Kiel
    • Rösler U. 1999 The X ln X condition for the weighted branching process. Technical Report, University of Kiel.
    • (1999)
    • Rösler, U.1
  • 34
    • 0002015483 scopus 로고    scopus 로고
    • The contraction method for recursive algorithms
    • Rösler U. Rüschendorf L. The contraction method for recursive algorithms Algorithmica 29 2001 3-33
    • (2001) Algorithmica , vol.29 , pp. 3-33
    • Rösler, U.1    Rüschendorf, L.2
  • 36
    • 26744456742 scopus 로고    scopus 로고
    • The rate of convergence for weighted branching processes
    • Technical Report, University of Kiel
    • Rösler U. Topchii V.A. Vatutin V.A. 2001 The rate of convergence for weighted branching processes. Technical Report, University of Kiel.
    • (2001)
    • Rösler, U.1    Topchii, V.A.2    Vatutin, V.A.3
  • 37
    • 0000320008 scopus 로고
    • On branching processes in random environments
    • Smith W.L. Wilkinson W.E. On branching processes in random environments Ann. Math. Statist. 40 1969 814-827
    • (1969) Ann. Math. Statist. , vol.40 , pp. 814-827
    • Smith, W.L.1    Wilkinson, W.E.2
  • 38
    • 0013206510 scopus 로고
    • A zero-one law for stationary sequences
    • Tanny D. A zero-one law for stationary sequences Z. Wahrsch. Verw. Gebiete 30 1974 139-148
    • (1974) Z. Wahrsch. Verw. Gebiete , vol.30 , pp. 139-148
    • Tanny, D.1
  • 39
    • 0242641708 scopus 로고
    • Limit theorems for branching processes in a random environment
    • Tanny D. Limit theorems for branching processes in a random environment Ann. Probab. 5 1977 100-116
    • (1977) Ann. Probab. , vol.5 , pp. 100-116
    • Tanny, D.1
  • 40
    • 0242556958 scopus 로고
    • Normalizing constants for branching processes in random environments (B.P.R.E.)
    • Tanny D. Normalizing constants for branching processes in random environments (B.P.R.E.) Stoch. Proc. Appl. 6 1978 201-211
    • (1978) Stoch. Proc. Appl. , vol.6 , pp. 201-211
    • Tanny, D.1
  • 41
    • 0011611270 scopus 로고
    • On multitype branching processes in a random environment
    • Tanny D. On multitype branching processes in a random environment Adv. Appl. Probab. 13 1981 464-497
    • (1981) Adv. Appl. Probab. , vol.13 , pp. 464-497
    • Tanny, D.1
  • 42
    • 38249032163 scopus 로고
    • A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means
    • Tanny D. A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means Stochastic Process. Appl. 28 1988 123-139
    • (1988) Stochastic Process. Appl. , vol.28 , pp. 123-139
    • Tanny, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.