메뉴 건너뛰기




Volumn 95, Issue 1, 2001, Pages 83-107

Asymptotic properties and absolute continuity of laws stable by random weighted mean

Author keywords

60F05, 60F15; 60K35; Branching processes; Branching random walks; Crump Mode Jagers; Functional equations; Left tails; Martingales; Moments of negative orders; Multiplicative cascades; Primary 60J80, 60G57; Secondary 60G42, 60E10, 60G30; Smoothing processes

Indexed keywords


EID: 0012585124     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(01)00092-8     Document Type: Article
Times cited : (77)

References (46)
  • 1
    • 0000988252 scopus 로고
    • On the supercritical one dimensional age dependent branching processes
    • Athreya K.B. On the supercritical one dimensional age dependent branching processes. Ann. Math. Statist. 40:1969;743-763.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 743-763
    • Athreya, K.B.1
  • 2
    • 84968498660 scopus 로고
    • On the absolute continuity of the limit random variable in the supercritical Galton-Watson branching process
    • Athreya K.B. On the absolute continuity of the limit random variable in the supercritical Galton-Watson branching process. Proc. Amer. Math. Soc. 30:1971;563-565.
    • (1971) Proc. Amer. Math. Soc. , vol.30 , pp. 563-565
    • Athreya, K.B.1
  • 5
    • 0005122705 scopus 로고    scopus 로고
    • Une extension de l'quation fonctionnelle de B. Mandelbrot
    • Barral J. Une extension de l'quation fonctionnelle de B. Mandelbrot. C. R. Acad. Sci. Paris Sr. I. 326:1998;421-426.
    • (1998) C. R. Acad. Sci. Paris Sr. I , vol.326 , pp. 421-426
    • Barral, J.1
  • 6
    • 0040120482 scopus 로고    scopus 로고
    • Moments, continuité, et analyse multifractale des cascades multiplicatives de Mandelbrot
    • Barral J. Moments, continuité, et analyse multifractale des cascades multiplicatives de Mandelbrot. Probab. Theory Related Fields. 113:1999;535-569.
    • (1999) Probab. Theory Related Fields , vol.113 , pp. 535-569
    • Barral, J.1
  • 7
    • 0002532950 scopus 로고
    • On age-dependent binary branching processes
    • Bellman R., Harris T. On age-dependent binary branching processes. Ann. Math. 55:1952;280-295.
    • (1952) Ann. Math. , vol.55 , pp. 280-295
    • Bellman, R.1    Harris, T.2
  • 8
    • 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
  • 9
    • 0018752527 scopus 로고
    • Continuity of limit random variables in the branching random walk
    • Biggins J.D., Grey D.R. Continuity of limit random 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
    • 0000459757 scopus 로고
    • On the limit of a supercritical branching process
    • Bingham N.H. On the limit of a supercritical branching process. J. Appl. Probab. 25A:1988;215-228.
    • (1988) J. Appl. Probab. , vol.25 , pp. 215-228
    • Bingham, N.H.1
  • 12
    • 0016358946 scopus 로고
    • Asymptotic properties of supercritical branching processes I: The Galton-Watson process
    • Bingham N.H., Doney R.A. Asymptotic properties of supercritical branching processes I: the Galton-Watson process. Adv. Appl. Probab. 6:1974;711-731.
    • (1974) Adv. Appl. Probab. , vol.6 , pp. 711-731
    • Bingham, N.H.1    Doney, R.A.2
  • 13
    • 0016487661 scopus 로고
    • Asymptotic properties of supercritical branching processes II: Crump-Mode and Jirina processes
    • Bingham N.H., Doney R.A. Asymptotic properties of supercritical branching processes II: Crump-Mode and Jirina processes. Adv. Appl. Probab. 7:1975;66-82.
    • (1975) Adv. Appl. Probab. , vol.7 , pp. 66-82
    • Bingham, N.H.1    Doney, R.A.2
  • 15
    • 0002525583 scopus 로고
    • Norming constants for the finite mean supercritical Bellman-Harris process
    • Cohn H. Norming constants for the finite mean supercritical Bellman-Harris process. Z. Wahrsch. 61:1982;189-205.
    • (1982) Z. Wahrsch. , vol.61 , pp. 189-205
    • Cohn, H.1
  • 16
    • 49949126877 scopus 로고
    • A general age-dependent branching process
    • 25, 8-17
    • Crump, K., Mode, C.J., 1968-1969. A general age-dependent branching process. J. Math. Anal. Appl. 24, 497-508, 25, 8-17.
    • (1968) J. Math. Anal. Appl. , vol.24 , pp. 497-508
    • Crump, K.1    Mode, C.J.2
  • 17
    • 0001463721 scopus 로고
    • A limit theorem for a class of supercritical branching processes
    • Doney R.A. A limit theorem for a class of supercritical branching processes. J. Appl. Probab. 9:1972;707-724.
    • (1972) J. Appl. Probab. , vol.9 , pp. 707-724
    • Doney, R.A.1
  • 18
    • 0001296692 scopus 로고
    • Problmes relatifs l'itration de fonctions suggrs par les processus en cascade
    • Dubuc S. Problmes relatifs l'itration de fonctions suggrs par les processus en cascade. Ann. Inst. Fourier Grenoble. 21:1971;171-251.
    • (1971) Ann. Inst. Fourier Grenoble , vol.21 , pp. 171-251
    • Dubuc, S.1
  • 19
    • 51249186049 scopus 로고
    • Fixed points of the smoothing transformation
    • Durrett R., Liggett T. Fixed points of the smoothing transformation. Z. Wahrsch. verw. Gebeite. 64:1983;275-301.
    • (1983) Z. Wahrsch. Verw. Gebeite , vol.64 , pp. 275-301
    • Durrett, R.1    Liggett, T.2
  • 20
    • 84968468564 scopus 로고
    • Cut set sums and tree processes
    • Falconer K.J. Cut set sums and tree processes. Proc. Amer. Math. Soc. (2). 101:1987;337-346.
    • (1987) Proc. Amer. Math. Soc. (2) , vol.101 , pp. 337-346
    • Falconer, K.J.1
  • 22
    • 0000517380 scopus 로고
    • Sur une extension de la notion de loi semi-stable
    • Guivarc'h Y. Sur une extension de la notion de loi semi-stable. Ann. Inst. Henri Poincar. 26:1990;261-285.
    • (1990) Ann. Inst. Henri Poincar , vol.26 , pp. 261-285
    • Guivarc'H, Y.1
  • 23
    • 0001090510 scopus 로고
    • Branching processes
    • Harris T.E. Branching processes. Ann. Math. Statist. 19:1948;474-494.
    • (1948) Ann. Math. Statist. , vol.19 , pp. 474-494
    • Harris, T.E.1
  • 25
    • 0000407851 scopus 로고
    • Generalized poltach and smoothing processes
    • Holley R., Liggett T. Generalized poltach and smoothing processes. Z. Wahrsch. verw. Gebeite. 55:1981;165-195.
    • (1981) Z. Wahrsch. Verw. Gebeite , vol.55 , pp. 165-195
    • Holley, R.1    Liggett, T.2
  • 26
    • 0000629694 scopus 로고
    • Multifractal dimensions and scaling exponents for strongly bounded cascades
    • Holley R., Waymire E.C. Multifractal dimensions and scaling exponents for strongly bounded cascades. Ann. Appl. Probab. 2:1992;819-845.
    • (1992) Ann. Appl. Probab. , vol.2 , pp. 819-845
    • Holley, R.1    Waymire, E.C.2
  • 27
    • 0000536984 scopus 로고
    • Produit de poids aléatoires indépendants et applications.
    • J. Bélaire, & S. Dubuc. Dordrecht: Kluwer Acad. Publ.
    • Kahane J.-P. Produit de poids aléatoires indépendants et applications. Bélaire J., Dubuc S. Fractal Geometry and Analysis. 1991;277-324 Kluwer Acad. Publ. Dordrecht.
    • (1991) Fractal Geometry and Analysis , pp. 277-324
    • Kahane, J.-P.1
  • 28
    • 0003329153 scopus 로고
    • Sur certaines martingales de Benoit Mandelbrot
    • Kahane, J.P., Peyrière, 1976. Sur certaines martingales de Benoit Mandelbrot. Adv. Math. 22, 131-145.
    • (1976) Adv. Math. , vol.22 , pp. 131-145
    • Kahane, J.P.1    Peyrière2
  • 29
    • 0012027321 scopus 로고
    • Tauberian theorems of exponential type
    • Kasahara Y. Tauberian theorems of exponential type. J. Math. Kyoto Univ. (JMK YAZ). 18:1978;209-219.
    • (1978) J. Math. Kyoto Univ. (JMK YAZ) , vol.18 , pp. 209-219
    • Kasahara, Y.1
  • 30
    • 0002508627 scopus 로고
    • A limit theorem for multidimensional Galton-Watson processes
    • Kesten H., Stigum B.P. A limit theorem for multidimensional Galton-Watson processes. Ann. Math. Statist. 37:1966;1211-1223.
    • (1966) Ann. Math. Statist. , vol.37 , pp. 1211-1223
    • Kesten, H.1    Stigum, B.P.2
  • 31
    • 0032251048 scopus 로고    scopus 로고
    • Slow variation and uniqueness of solutions to the functional equation in the branching random walk
    • Kyprianou A. Slow variation and uniqueness of solutions to the functional equation in the branching random walk. J. Appl. Probab. 35:1998;795-801.
    • (1998) J. Appl. Probab. , vol.35 , pp. 795-801
    • Kyprianou, A.1
  • 33
    • 0012911035 scopus 로고    scopus 로고
    • The growth of an entire characteristic function and the tail probability of the limit of a tree martingale
    • In: Chauvin, B., Cohen, S., Rouault, A. (Eds.) Birkhäuser, Basel
    • Liu, Q.S., 1996. The growth of an entire characteristic function and the tail probability of the limit of a tree martingale. In: Chauvin, B., Cohen, S., Rouault, A. (Eds.), Trees, Progress in Probability, Vol. 40, Birkhäuser, Basel, pp. 51-80.
    • (1996) Trees, Progress in Probability , vol.40 , pp. 51-80
    • Liu, Q.S.1
  • 34
    • 3342908453 scopus 로고    scopus 로고
    • Sur une équation fonctionnelle et ses applications: Une extension du théorème de Kesten-Stigum concernant des processus de branchement
    • Liu Q.S. Sur une équation fonctionnelle 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.S.1
  • 35
    • 0032025081 scopus 로고    scopus 로고
    • Fixed points of a generalized smoothing transformation and applications to branching processes
    • Liu Q.S. Fixed points of a generalized smoothing transformation and applications to branching processes. Adv. Appl. Probab. 30:1998;85-112.
    • (1998) Adv. Appl. Probab. , vol.30 , pp. 85-112
    • Liu, Q.S.1
  • 36
    • 0002649784 scopus 로고    scopus 로고
    • Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks
    • Liu Q.S. 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.S.1
  • 38
    • 0001019904 scopus 로고    scopus 로고
    • On generalized multiplicative cascades
    • Liu Q.S. On generalized multiplicative cascades. Stochastic Process. Appl. 86:2000;263-286.
    • (2000) Stochastic Process. Appl. , vol.86 , pp. 263-286
    • Liu, Q.S.1
  • 40
    • 0008984822 scopus 로고    scopus 로고
    • A simple path to Biggins's martingale convergence for branching random walk
    • In: Athreya, K.B., Jagers, P. (Eds.) Springer, Berlin
    • Lyons, R., 1997. A simple path to Biggins's martingale convergence for branching random walk. In: Athreya, K.B., Jagers, P. (Eds.), Classical and Modern Branching Processes, IMA Volumes in Mathematics and its Applications, Vol. 84, Springer, Berlin, pp. 217-221.
    • (1997) Classical and Modern Branching Processes, IMA Volumes in Mathematics and Its Applications , vol.84 , pp. 217-221
    • Lyons, R.1
  • 41
    • 0001287197 scopus 로고
    • Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire
    • 355-358
    • Mandelbrot, B., 1974. Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire. C. R. Acad. Sci. Paris Ser.I 278, 289-292, 355-358.
    • (1974) C. R. Acad. Sci. Paris Ser.I , vol.278 , pp. 289-292
    • Mandelbrot, B.1
  • 42
    • 0030239983 scopus 로고    scopus 로고
    • Scaling exponents and multifractal dimensions for independent random cascades
    • Molchan G.M. Scaling exponents and multifractal dimensions for independent random cascades. Comm. Math. Phys. 179:1996;681-702.
    • (1996) Comm. Math. Phys. , vol.179 , pp. 681-702
    • Molchan, G.M.1
  • 43
    • 84972584760 scopus 로고
    • Calcul de dimensions de Hausdorff
    • Peyrière J. Calcul de dimensions de Hausdorff. Duke Math. J. 44:1977;591-601.
    • (1977) Duke Math. J. , vol.44 , pp. 591-601
    • Peyrière, J.1
  • 44
    • 38249008257 scopus 로고
    • A fixed point theorem for distributions
    • Rösler U. A fixed point theorem for distributions. Stochastic Process. Appl. 42:1992;195-214.
    • (1992) Stochastic Process. Appl. , vol.42 , pp. 195-214
    • Rösler, U.1
  • 45
    • 0002580644 scopus 로고
    • Seneta constants for the supercritical Bellman-Harris process
    • Schuh H.J. Seneta constants for the supercritical Bellman-Harris process. Adv. Appl. Probab. 14:1982;732-751.
    • (1982) Adv. Appl. Probab. , vol.14 , pp. 732-751
    • Schuh, H.J.1
  • 46
    • 84911664192 scopus 로고
    • A theorem on the Galton-Watson process
    • Stigum B.P. A theorem on the Galton-Watson process. Ann. Math. Statist. 37:1966;696-698.
    • (1966) Ann. Math. Statist. , vol.37 , pp. 696-698
    • Stigum, B.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.