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Volumn 114, Issue 1, 2004, Pages 27-50

Elementary fixed points of the BRW smoothing transforms with infinite number of summands

Author keywords

Branching random walk; Contraction principle; Fixed points; Perpetuity; Regular variation; Smoothing transform

Indexed keywords


EID: 4644286698     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.06.002     Document Type: Article
Times cited : (41)

References (38)
  • 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
    • 9844243443 scopus 로고    scopus 로고
    • On a class of characterization problems for random convex combinations
    • Baringhaus L. Grübel R. On a class of characterization problems for random convex combinations Ann. Inst. Statist. Math. 49 1997 555-567
    • (1997) Ann. Inst. Statist. Math. , vol.49 , pp. 555-567
    • Baringhaus, L.1    Grübel, R.2
  • 3
    • 4644364035 scopus 로고    scopus 로고
    • Asymptotic laws for nonconservative self-similar fragmentations
    • Preprint, available online at
    • J. Bertoin, A.V. Gnedin, Asymptotic laws for nonconservative self-similar fragmentations, Preprint, available online at http://www.arxiv.org/abs/math.PR/0402227, 2004
    • (2004)
    • Bertoin, J.1    Gnedin, A.V.2
  • 4
    • 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
  • 5
    • 3342944866 scopus 로고    scopus 로고
    • Branching random walk: Seneta-Heyde norming
    • B. Chauvin, Cohen, S. A. Rouault (Eds.), June 14-16, 1995, Birkhauser, Basel
    • J.D. Biggins, A.E. Kyprianou, Branching random walk: Seneta-Heyde norming, in: B. Chauvin, S. Cohen, A. Rouault (Eds.), Trees: Proceedings of a Workshop in Versailles, June 14-16, 1995, Birkhauser, Basel, 1996, pp. 31-50
    • (1996) Trees: Proceedings of a Workshop in Versailles , pp. 31-50
    • Biggins, J.D.1    Kyprianou, A.E.2
  • 6
    • 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
  • 7
    • 4644270612 scopus 로고    scopus 로고
    • Fixed points of the smoothing transform; the boundary case
    • Preprint, available online at
    • J.D. Biggins, A.E. Kyprianou, Fixed points of the smoothing transform; the boundary case, Preprint, available online at http://www.math.uu.nl/people/kypriano/smoothing.pdf, 2003
    • (2003)
    • Biggins, J.D.1    Kyprianou, A.E.2
  • 9
    • 0003571205 scopus 로고
    • Regular Variation
    • Cambridge: Cambridge University Press
    • Bingham N.H. Goldie C.M. Teugels J.L. Regular Variation 1989 Cambridge University Press Cambridge
    • (1989)
    • Bingham, N.H.1    Goldie, C.M.2    Teugels, J.L.3
  • 10
    • 0037706919 scopus 로고    scopus 로고
    • Symmetric fixed points of a smoothing transformation
    • Caliebe A. Symmetric fixed points of a smoothing transformation Adv. Appl. Probab. 35 2003 377-394
    • (2003) Adv. Appl. Probab. , vol.35 , pp. 377-394
    • Caliebe, A.1
  • 11
    • 0041841605 scopus 로고    scopus 로고
    • Fixed points with finite variance of a smoothing transformation
    • Caliebe A. Rösler U. Fixed points with finite variance of a smoothing transformation Stochastic Process. Appl. 107 2003 105-129
    • (2003) Stochastic Process. Appl. , vol.107 , pp. 105-129
    • Caliebe, A.1    Rösler, U.2
  • 12
    • 77953820863 scopus 로고    scopus 로고
    • Fixed points of a smoothing transformation with finite expectation: Closing a gap
    • Preprint, available online at
    • A. Caliebe, U. Rösler, Fixed points of a smoothing transformation with finite expectation: closing a gap, Preprint, available online at http://www-computerlabor.math.uni-kiel.de/stochastik/caliebe/ Preprint.pdf, 2003
    • (2003)
    • Caliebe, A.1    Rösler, U.2
  • 13
    • 51249186049 scopus 로고
    • Fixed points of the smoothing transformation
    • Durrett R. Liggett T. Fixed points of the smoothing transformation Z. Wahrsch. 64 1983 275-301
    • (1983) Z. Wahrsch. , vol.64 , pp. 275-301
    • Durrett, R.1    Liggett, T.2
  • 14
    • 0000732230 scopus 로고
    • Implicit renewal theory and tails of solutions of random equations
    • Goldie C.M. Implicit renewal theory and tails of solutions of random equations Ann. Appl. Probab. 1 1991 126-166
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 126-166
    • Goldie, C.M.1
  • 15
    • 0034214584 scopus 로고    scopus 로고
    • Stability of perpetuities
    • Goldie C.M. Maller R.A. Stability of perpetuities Ann. Probab. 28 2000 1195-1218
    • (2000) Ann. Probab. , vol.28 , pp. 1195-1218
    • Goldie, C.M.1    Maller, R.A.2
  • 16
    • 0012486329 scopus 로고
    • One limit distribution for a random walk on the line
    • Grincevičius A.K. One limit distribution for a random walk on the line Lithuanian Math. J. 15 1975 580-589
    • (1975) Lithuanian Math. J. , vol.15 , pp. 580-589
    • Grincevičius, A.K.1
  • 17
    • 0000517380 scopus 로고
    • Sur une extension de la notion semi-stable
    • Guivarc'h Y. Sur une extension de la notion semi-stable Ann. Inst. Henri Poincaré. 26 1990 261-285
    • (1990) Ann. Inst. Henri Poincaré , vol.26 , pp. 261-285
    • Guivarc'h, Y.1
  • 18
    • 0037360623 scopus 로고    scopus 로고
    • Thick and thin points for random recursive fractals
    • Hambly B.M. Jones O.D. Thick and thin points for random recursive fractals Adv. Appl. Probab. 35 2003 251-277
    • (2003) Adv. Appl. Probab. , vol.35 , pp. 251-277
    • Hambly, B.M.1    Jones, O.D.2
  • 19
    • 4644283646 scopus 로고    scopus 로고
    • p-convergence of branching-duffusion martingales
    • Mathematics Preprint. 0405, University of Bath. Available online at
    • p-convergence of branching-duffusion martingales. Mathematics Preprint. 0405, University of Bath. Available online at http://www.bath.ac.uk/~massch/Research/Papers/spine-Lp-cgce.pdf, 2004
    • (2004)
    • Hardy, R.1    Harris, S.C.2
  • 20
    • 0343772976 scopus 로고    scopus 로고
    • Random fractal measures and probability metrics
    • Hutchinson J.E. Rüschendorf L. Random fractal measures and probability metrics Adv. Appl. Probab. 32 2000 925-947
    • (2000) Adv. Appl. Probab. , vol.32 , pp. 925-947
    • Hutchinson, J.E.1    Rüschendorf, L.2
  • 21
    • 2342530628 scopus 로고    scopus 로고
    • On positive distribution of the class L of self-decomposable laws
    • Iksanov A.M. On positive distribution of the class L of self-decomposable laws Theor. Probab. Math. Statist. 64 2002 51-61
    • (2002) Theor. Probab. Math. Statist. , vol.64 , pp. 51-61
    • Iksanov, A.M.1
  • 22
    • 2342520951 scopus 로고    scopus 로고
    • On perpetuities related to the size-based distributions
    • Iksanov A.M. On perpetuities related to the size-based distributions Theory Stochastic Process 24 2002 128-135
    • (2002) Theory Stochastic Process , vol.24 , pp. 128-135
    • Iksanov, A.M.1
  • 23
    • 0036950492 scopus 로고    scopus 로고
    • On fixed points of Poisson shot noise transforms
    • Iksanov A.M. Jurek Z.J. On fixed points of Poisson shot noise transforms Adv. Appl. Probab. 34 2002 798-825
    • (2002) Adv. Appl. Probab. , vol.34 , pp. 798-825
    • Iksanov, A.M.1    Jurek, Z.J.2
  • 25
    • 2342448210 scopus 로고    scopus 로고
    • New explicit examples of fixed points of Poisson shot noise transforms
    • Iksanov A.M. Kim C.S. New explicit examples of fixed points of Poisson shot noise transforms Austral. New Zealand J. Statist. 46 2004 313-321
    • (2004) Austral. New Zealand J. Statist. , vol.46 , pp. 313-321
    • Iksanov, A.M.1    Kim, C.S.2
  • 26
    • 2942672026 scopus 로고
    • Random difference equations and renewal theory for products of random matrices
    • Kesten H. Random difference equations and renewal theory for products of random matrices Acta. Math. 131 1973 207-248
    • (1973) Acta. Math. , vol.131 , pp. 207-248
    • Kesten, H.1
  • 27
    • 0003334918 scopus 로고    scopus 로고
    • Two renewal theorems for general random walks tending to infinity
    • Kesten H. Maller R.A. Two renewal theorems for general random walks tending to infinity Probab. Theory Related Fields 106 1996 1-38
    • (1996) Probab. Theory Related Fields , vol.106 , pp. 1-38
    • Kesten, H.1    Maller, R.A.2
  • 28
    • 3342908453 scopus 로고    scopus 로고
    • Sur une équation fonctionnelle et ses applications: Une extension du théoréme de Kesten-Stigum concernant des processus de branchement
    • Liu Q. Sur une équation fonctionnelle et ses applications: une extension du théoréme 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
  • 29
    • 0032025081 scopus 로고    scopus 로고
    • Fixed points of a generalized smoothing transformation and applications to the branching random walk
    • Liu Q. Fixed points of a generalized smoothing transformation 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
  • 30
    • 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
  • 31
    • 0008984822 scopus 로고    scopus 로고
    • A simple path to Biggins's martingale convergence for branching random walk
    • K.B. Athreya, P. Jagers (Eds.), Springer, Berlin
    • R. Lyons, A simple path to Biggins's martingale convergence for branching random walk, in: K.B. Athreya, P. Jagers (Eds.), Classical and Modern Branching Processes, IMA Volumes in Mathematics and its Applications, Vol. 84, Springer, Berlin, 1997, pp. 217-221
    • (1997) Classical and Modern Branching Processes, IMA Volumes in Mathematics and Its Applications , vol.84 , pp. 217-221
    • Lyons, R.1
  • 33
    • 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
  • 34
    • 0037959953 scopus 로고    scopus 로고
    • Infinitely divisible laws associated with hyperbolic functions
    • Pitman J. Yor M. Infinitely divisible laws associated with hyperbolic functions Canad. J. Math. 55 2003 292-330
    • (2003) Canad. J. Math. , vol.55 , pp. 292-330
    • Pitman, J.1    Yor, M.2
  • 35
    • 0001131997 scopus 로고
    • Probability metrics and recursive algorithms
    • Rachev S.T. Rüschendorf L. Probability metrics and recursive algorithms Adv. Appl. Probab. 27 1995 770-799
    • (1995) Adv. Appl. Probab. , vol.27 , pp. 770-799
    • Rachev, S.T.1    Rüschendorf, L.2
  • 37
    • 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
  • 38
    • 0004044683 scopus 로고    scopus 로고
    • Lévy Processes and Infinitely Divisible Distributions
    • Cambridge: Cambridge University Press
    • Sato K. Lévy Processes and Infinitely Divisible Distributions 1999 Cambridge University Press Cambridge
    • (1999)
    • Sato, K.1


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