메뉴 건너뛰기




Volumn 10, Issue 1, 2000, Pages 218-239

Limit theorems for Mandelbrot's multiplicative cascades

Author keywords

Central limit theorem; Convergence of moment generating function; Large deviations; Law of large numbers; Mandelbrot's martingales; Self similar cascades

Indexed keywords


EID: 0034344298     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1019737670     Document Type: Article
Times cited : (14)

References (19)
  • 2
    • 0001483086 scopus 로고
    • Large deviations in the supercritical branching process
    • BIGGINS, J. D. and BINGHAM, N. H. (1993). Large deviations in the supercritical branching process. Adv. in Appl. Prob. 25 757-772.
    • (1993) Adv. in Appl. Prob. , vol.25 , pp. 757-772
    • Biggins, J.D.1    Bingham, N.H.2
  • 5
    • 51249186049 scopus 로고
    • Fixed points of the smoothing transformation
    • DURRETT, R. and LIGGETT, T. (1983). Fixed points of the smoothing transformation. Z. Wahrsch. Verw. Gebeite 64 275-301.
    • (1983) Z. Wahrsch. Verw. Gebeite , vol.64 , pp. 275-301
    • Durrett, R.1    Liggett, T.2
  • 7
    • 0020021694 scopus 로고
    • Flow in networks with random capacities
    • GRIMMETT, G. R. and WELSH, D. J. A. (1982). Flow in networks with random capacities. Stochastics 7 205-229.
    • (1982) Stochastics , vol.7 , pp. 205-229
    • Grimmett, G.R.1    Welsh, D.J.A.2
  • 8
  • 9
    • 0000629694 scopus 로고
    • Multifractal dimensions and scaling exponents for strongly bounded cascades
    • HOLLEY, R. and WAYMIRE, E. C. (1992). Multifractal dimensions and scaling exponents for strongly bounded cascades. Ann. Appl. Prob. 2 819-845.
    • (1992) Ann. Appl. Prob. , vol.2 , pp. 819-845
    • Holley, R.1    Waymire, E.C.2
  • 10
    • 0003329153 scopus 로고
    • Sur certaines martingales de Benoit Mandelbrot
    • KAHANE, J. P. and PEYRIÈRE, J. (1976). Sur certaines martingales de Benoit Mandelbrot. Adv. Math. 22 131-145.
    • (1976) Adv. Math. , vol.22 , pp. 131-145
    • Kahane, J.P.1    Peyrière, J.2
  • 11
    • 0012911035 scopus 로고    scopus 로고
    • The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale
    • (B. Chauvin, S. Cohen and A. Rouault, eds) Birkhäuser, Boston
    • LIU, Q. S. (1996). The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale. In Trees (B. Chauvin, S. Cohen and A. Rouault, eds) 51-80. Birkhäuser, Boston.
    • (1996) Trees , pp. 51-80
    • Liu, Q.S.1
  • 12
    • 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. (1997a). Sur une équation fonctionnelle et ses applications: une extension du théorème de Kesten-Stigum concernant des processus de branchement. Adv. in Appl. Probab. 29 353-373.
    • (1997) Adv. in Appl. Probab. , vol.29 , pp. 353-373
    • Liu, Q.S.1
  • 13
    • 0002226656 scopus 로고    scopus 로고
    • On generalized multiplicative cascades
    • To appear
    • LIU, Q. S. (1997b). On generalized multiplicative cascades. Stochastic Process Appl. To appear.
    • (1997) Stochastic Process Appl.
    • Liu, Q.S.1
  • 14
    • 0032025081 scopus 로고    scopus 로고
    • Fixed points of a generalized smoothing transformation and applications to branching random walks
    • LIU, Q. S. (1998). Fixed points of a generalized smoothing transformation and applications to branching random walks. Adv. in Appl. Probab. 30 85-112.
    • (1998) Adv. in Appl. Probab. , vol.30 , pp. 85-112
    • Liu, Q.S.1
  • 15
    • 0002309545 scopus 로고    scopus 로고
    • Limit theorems for multiplicative processes
    • LAMA, Université de Versailles-Saint Quentin. To appear
    • LIU, Q. S. and ROUAULT, A. (1999). Limit theorems for multiplicative processes. Prépublication 32-99, LAMA, Université de Versailles-Saint Quentin. To appear.
    • (1999) Prépublication , pp. 32-99
    • Liu, Q.S.1    Rouault, A.2
  • 16
    • 0001287197 scopus 로고
    • Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire
    • MANDELBROT, B. (1974a). 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
  • 17
    • 0015969022 scopus 로고
    • Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier
    • MANDELBROT, B. (1974b). Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62 331-333.
    • (1974) J. Fluid Mech. , vol.62 , pp. 331-333
    • Mandelbrot, B.1
  • 18
    • 38249008257 scopus 로고
    • A fixed point theorem for distributions
    • RÖSLER, U. (1992). A fixed point theorem for distributions. Stochastic. Process Appl. 42 195-214.
    • (1992) Stochastic. Process Appl. , vol.42 , pp. 195-214
    • Rösler, U.1
  • 19
    • 0008319753 scopus 로고
    • Multiplicative cascades: Dimension spectra and dependence
    • Kahane Special Issue
    • WAYMIRE, E. C. and WILLIAMS, S. C. (1995). Multiplicative cascades: dimension spectra and dependence. J. Fourier Anal. Appl. (Kahane Special Issue) 589-609.
    • (1995) J. Fourier Anal. Appl. , pp. 589-609
    • Waymire, E.C.1    Williams, S.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.