Tail behavior of solutions of linear recursions on trees

Stochastic Processes and their Applications

Volumn 122, Issue 4, 2012, Pages 1777-1807

  Olvera Cravioto, Mariana ^a  

^a Department of Earth and Environmental Sciences   (United States)

Author keywords

Large deviations; Multiplicative cascades; Random difference equations; Regular variation; Stochastic fixed point equations; Stochastic recursions; Weighted branching processes

Indexed keywords

BRANCHING PROCESS; FIXED POINT EQUATION; LARGE DEVIATIONS; MULTIPLICATIVE CASCADES; RECURSIONS; REGULAR VARIATIONS;

DIFFERENCE EQUATIONS;

STOCHASTIC SYSTEMS;

EID: 84858729572     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2012.01.003     Document Type: Article

References (27)

1. D.J. Aldous, and A. Bandyopadhyay A survey of max-type recursive distributional equation Ann. Appl. Probab. 15 2 2005 1047 1110
2. G. Alsmeyer, J.D. Biggins, M. Meiners, The functional equation of the smoothing transform, Ann. Probab. (2010) (in press). arXiv:0906.3133.
3. G. Alsmeyer, M. Meiners, Fixed points of the smoothing transform: two-sided solutions, Probab. Theory Related Fields (2010)(under review) arXiv:1009.2412.
4. J.D. Biggins Martingale convergence in the branching random walk J. Appl. Probab. 14 1 1977 25 37
5. P. Billingsley Probability and Measure third ed. 1995 Wiley-Interscience New York
6. N.H. Bingham, C.M. Goldie, and J.L. Teugels Regular Variation 1987 Cambridge University Press Cambridge
7. bn with stationary coefficients Adv. Appl. Probab. 18 1 1986 211 220
8. S. Brin, and L. Page The anatomy of a large-scale hypertextual web search engine Comput. Netw. ISDN Syst. 30 1-7 1998 107 117
9. J.A. Fill, and S. Janson Approximating the limiting quicksort distribution Random Structures Algorithms 19 3-4 2001 376 406
10. C.M. Goldie Implicit renewal theory and tails of solutions of random equations Ann. Appl. Probab. 1 1 1991 126 166
11. C.M. Goldie, and R. Grbel Perpetuities with thin tails Adv. Appl. Probab. 28 2 1996 463 480
12. D.R. Grey Regular variation in the tail behaviour of solutions of random difference equations Ann. Appl. Probab. 4 1 1994 169 183
13. A.M. Iksanov Elementary fixed points of the BRW smoothing transforms with infinite number of summands Stochastic Process. Appl. 114 2004 27 50
14. P.R. Jelenkovi, and M. Olvera-Cravioto Information ranking and power laws on trees Adv. Appl. Probab. 42 2 2010 1057 1093
15. P.R. Jelenkovi, M. Olvera-Cravioto, Implicit renewal theorem for trees with general weights, 2011. arXiv:1012.2165.
16. P.R. Jelenkovi, and M. Olvera-Cravioto Implicit renewal theory on trees Adv. Appl. Probab. 44 2 2012 arXiv:1006.3295
17. A.H. Jessen, and T. Mikosch Regularly varying functions Publ. Inst. Math. (NS) 80 94 2006 171 192
18. H. Kesten Random difference equations and renewal theory for products of random matrices Acta Math. 131 1973 207 248
19. D.G. Konstantinides, and T. Mikosch Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovations Ann. Probab. 33 5 2005 1992 2035
20. Q. Liu On generalized multiplicative cascades Stochastic Process. Appl. 86 2000 263 286
21. R. Neininger, and L. Rschendorf A general limit theorem for recursive algorithms and combinatorial structures Ann. Appl. Probab. 14 1 2004 378 418
22. M. Olvera-Cravioto, Asymptotics for weighted random sums, 2011. arXiv:1102.0301.
23. U. Rsler The weighted branching process Dynamics of Complex and Irregular Systems Bielefeld, 1991 Bielefeld Encounters in Mathematics and Physics VIII 1993 World Science Publishing River Edge, NJ 154 165
24. U. Rsler, and L. Rschendorf The contraction method for recursive algorithms Algorithmica 29 1-2 2001 3 33
25. R. van der Hofstad, G. Hooghiemstra, and P. Van Mieghem Distances in random graphs with finite variance degrees Random Structures Algorithms 27 1 2005 76 123
26. Y. Volkovich, and N. Litvak Asymptotic analysis for personalized web search Adv. Appl. Probab. 42 2 2010 577 604
27. Y. Volkovich, N. Litvak, D. Donato, Determining factors behind the pagerank log-log plot, in: Proceedings of the 5th International Workshop on Algorithms and Models for the Web-Graph, WAW 2007, 2007.