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Volumn 10, Issue , 2005, Pages 609-631

Fixed points of the smoothing transform: The boundary case

Author keywords

Branching random walk; Functional equation; Smoothing transform

Indexed keywords


EID: 21244451201     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v10-255     Document Type: Article
Times cited : (74)

References (27)
  • 2
    • 0002244969 scopus 로고
    • Martingale convergence in the branching random walk
    • Biggins, J.D. (1977). Martingale convergence in the branching random walk. J. Appl. Probab. 14, 25-37.
    • (1977) J. Appl. Probab , vol.14 , pp. 25-37
    • Biggins, J.D.1
  • 3
    • 0040163973 scopus 로고    scopus 로고
    • Lindley-type equations in the branching random walk
    • Biggins, J.D. (1998). Lindley-type equations in the branching random walk. Stoch. Proc. Appl. 75, 105-133.
    • (1998) Stoch. Proc. Appl , vol.75 , pp. 105-133
    • Biggins, J.D.1
  • 4
    • 0031496422 scopus 로고    scopus 로고
    • Seneta-Heyde norming in the branching random walk
    • Biggins, J.D. And Kyprianou, A.E. (1997). Seneta-Heyde norming in the branching random walk. Ann. Probab. 25, 337-360.
    • (1997) Ann. Probab , vol.25 , pp. 337-360
    • Biggins, J.D.1    Kyprianou, A.E.2
  • 5
    • 3142665516 scopus 로고    scopus 로고
    • Measure change in multitype branching
    • Biggins, J.D. And Kyprianou, A.E. (2004). Measure change in multitype branching. Adv. Appl. Probab. 36, 544-581.
    • (2004) Adv. Appl. Probab , vol.36 , pp. 544-581
    • Biggins, J.D.1    Kyprianou, A.E.2
  • 6
    • 0016487661 scopus 로고
    • Asymptotic properties of supercritical branching processes. II: Crump-Mode and Jirana processes
    • Bingham, N. And Doney, R.A. (1975). Asymptotic properties of supercritical branching processes. II: Crump-Mode and Jirana processes. Adv. Appl. Probab. 7, 66-82.
    • (1975) Adv. Appl. Probab , vol.7 , pp. 66-82
    • Bingham, N.1    Doney, R.A.2
  • 7
    • 84980189802 scopus 로고
    • Maximal displacement of branching Brownian motion
    • Bramson, M. (1979). Maximal displacement of branching Brownian motion. Comm. Pure Appl. Math. 31, 531-581.
    • (1979) Comm. Pure Appl. Math , vol.31 , pp. 531-581
    • Bramson, M.1
  • 8
    • 0003175686 scopus 로고
    • Convergence of solutions of the Kolmogorov non linear diffusion equations to travelling waves
    • Bramson, M. (1983). Convergence of solutions of the Kolmogorov non linear diffusion equations to travelling waves. Mem. Amer. Math. Soc. 44(285).
    • (1983) Mem. Amer. Math. Soc , vol.44 , Issue.285
    • Bramson, M.1
  • 9
    • 0037706919 scopus 로고    scopus 로고
    • Symmetric fixed points of a smoothing transfor mation
    • Caliebe, A. (2003). Symmetric fixed points of a smoothing transfor mation. Adv. Appl. Probab. 35, 377-394.
    • (2003) Adv. Appl. Probab , vol.35 , pp. 377-394
    • Caliebe, A.1
  • 10
    • 0041841605 scopus 로고    scopus 로고
    • Fixed points with finite variance of a smoothing transform
    • Caliebe, A. And Rösler, U. (2003a). Fixed points with finite variance of a smoothing transform. Stoc. Proc. Appl. 107, 105-129.
    • (2003) Stoc. Proc. Appl , vol.107 , pp. 105-129
    • Caliebe, A.1    Rösler, U.2
  • 11
    • 51249186049 scopus 로고
    • Fixed points of the smoothing transform
    • Durrett, R. And Liggett, M. (1983). Fixed points of the smoothing transform. Z. Wahrsch. verw. Gebiete 64, 275-301.
    • (1983) Z. Wahrsch. Verw. Gebiete , vol.64 , pp. 275-301
    • Durrett, R.1    Liggett, M.2
  • 13
    • 0034264825 scopus 로고    scopus 로고
    • On the lattice case of an almost-sure renewal theorem for branching random walks
    • Gatzouras, D. (2000). On the lattice case of an almost-sure renewal theorem for branching random walks. Adv. Appl. Probab. 32,720-737.
    • (2000) Adv. Appl. Probab , vol.32 , pp. 720-737
    • Gatzouras, D.1
  • 14
    • 22644449518 scopus 로고    scopus 로고
    • Travelling waves for the FKPP equation via probabilistic arguments
    • Harris, S.C. (1999). Travelling waves for the FKPP equation via probabilistic arguments. Proc. Roy. Soc. Edin. 129A 503-517.
    • (1999) Proc. Roy. Soc. Edin , vol.129A , pp. 503-517
    • Harris, S.C.1
  • 15
    • 4644286698 scopus 로고    scopus 로고
    • Elementary fixed points of the BRW smoothing transforms with infinite number of summands
    • Iksanov, A.M. (2004). Elementary fixed points of the BRW smoothing transforms with infinite number of summands. Stoc. Proc. Appl. 114, 27-50.
    • (2004) Stoc. Proc. Appl , vol.114 , pp. 27-50
    • Iksanov, A.M.1
  • 16
    • 0036950492 scopus 로고    scopus 로고
    • On fixed points of Poisson shot noise transforms
    • Iksanov, A.M. And Jurek, Z.J. (2002). On fixed points of Poisson shot noise transforms. Adv. Appl. Probab. 34, 798-825.
    • (2002) Adv. Appl. Probab , vol.34 , pp. 798-825
    • Iksanov, A.M.1    Jurek, Z.J.2
  • 17
    • 0003329153 scopus 로고
    • Sur certaines martingales de Benoit Mandelbrot
    • Kahane, J.P. And Peyriere, 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    Peyriere, J.2
  • 18
    • 0032251048 scopus 로고    scopus 로고
    • Slow variation and uniqueness of solutions to the functional equation in the branching random walk
    • Kyprianou, A.E. (1998). Slow variation and uniqueness of solutions to the functional equation in the branching random walk. J. Appl. Probab. 35, 795-802.
    • (1998) J. Appl. Probab , vol.35 , pp. 795-802
    • Kyprianou, A.E.1
  • 19
    • 0742289230 scopus 로고    scopus 로고
    • Travelling wave solutions to the K-P-P equation: Alternatives to Simon Harris’ probabilistic analysis
    • Kyprianou, A.E. (2004). Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris’ probabilistic analysis. Ann. Inst. H. Poincaré Prob. Statist. 40, 53-72.
    • (2004) Ann. Inst. H. Poincaré Prob. Statist , vol.40 , pp. 53-72
    • Kyprianou, A.E.1
  • 20
    • 0032025081 scopus 로고    scopus 로고
    • Fixed points of a generalized smoothing transform and applications to the branching processes
    • Liu, Q. (1998). Fixed points of a generalized smoothing transform and applications to the branching processes. Adv. Appl. Probab. 30, 85112.
    • (1998) Adv. Appl. Probab , vol.30 , pp. 85112
    • Liu, Q.1
  • 21
    • 0001019904 scopus 로고    scopus 로고
    • On generalized multiplicative cascades
    • Liu, Q. (2000). On generalized multiplicative cascades. Stoc. Proc. Appl. 86, 263-286.
    • (2000) Stoc. Proc. Appl , vol.86 , pp. 263-286
    • Liu, Q.1
  • 22
    • 0008984822 scopus 로고    scopus 로고
    • A simple path to Biggins’ martingale convergence
    • (eds: K.B. Athreya, P. Jagers). IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York
    • Lyons, r. (1997). A simple path to Biggins’ martingale convergence. In Classical and Modern Branching Processes (eds: K.B. Athreya, P. Jagers). IMA Volumes in Mathematics and its Applications 84, 217-222. Springer-Verlag, New York.
    • (1997) Classical and Modern Branching Processes , vol.84 , pp. 217-222
    • Lyons, R.1
  • 23
    • 84980187449 scopus 로고
    • Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov
    • (Correction: (1976) 29, 553-554)
    • McKean, H.P. (1975). Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math. 28, 323-331. (Correction: (1976) 29, 553-554).
    • (1975) Comm. Pure Appl. Math , vol.28 , pp. 323-331
    • Mc Kean, H.P.1
  • 24
    • 0001491884 scopus 로고
    • On the convergence of supercritical general (C-M-J) branching process
    • Nerman, O. (1981). On the convergence of supercritical general (C-M-J) branching process. Z. Wahrsch. verw. Gebiete 57, 365-395.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.57 , pp. 365-395
    • Nerman, O.1
  • 25
    • 0040770634 scopus 로고
    • Multiplicative martingales for spatial branching processes
    • (eds: E. Cinlar, K.L. Chung, R.K. Getoor). Progress in Probability and Statistics, Birkhäuser, Boston
    • Neveu, J. (1988). Multiplicative martingales for spatial branching processes. In Seminar on Stochastic Processes, 1987, (eds: E. Cinlar, K.L. Chung, R.K. Getoor). Progress in Probability and Statistics, 15, 223-241. Birkhäuser, Boston.
    • (1988) Seminar on Stochastic Processes, 1987 , vol.15 , pp. 223-241
    • Neveu, J.1
  • 26
    • 84985545846 scopus 로고
    • On characterizations via mixed sums
    • Pakes, A.G. (1992). On characterizations via mixed sums. Austral. J. Statist. 34, 323-339.
    • (1992) Austral. J. Statist , vol.34 , pp. 323-339
    • Pakes, A.G.1
  • 27
    • 38249008257 scopus 로고
    • A fixed point theorem for distributions
    • Rosler, U. (1992). A fixed point theorem for distributions. Stoc. Proc. Appl. 42, 195-214
    • (1992) Stoc. Proc. Appl , vol.42 , pp. 195-214
    • Rosler, U.1


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