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  1. Arbeiter, Matthias. Random recursive construction of self-similar fractal measures. The noncompact case. Probab. Theory Related Fields 88 (1991), no. 4, 497--520. MR1105715 (92m:60040)
  2. Biggins, J. D. Uniform convergence of martingales in the branching random walk. Ann. Probab. 20 (1992), no. 1, 137--151. MR1143415 (93b:60094)
  3. Biggins, J. D.; Kyprianou, A. E. Seneta-Heyde norming in the branching random walk. Ann. Probab. 25 (1997), no. 1, 337--360. MR1428512 (98a:60118)
  4. Burton, Robert M.; Rösler, Uwe . An $Lsb 2$ convergence theorem for random affine mappings. J. Appl. Probab. 32 (1995), no. 1, 183--192. MR1316801 (96b:60011)
  5. Caliebe, Amke. Symmetric fixed points of a smoothing transformation. Adv. in Appl. Probab. 35 (2003), no. 2, 377--394. MR1970480 (2004f:60036)
  6. Choquet, Gustave; Deny, Jacques. Sur l'équation de convolution $µ=µ*sigma $. (French) C. R. Acad. Sci. Paris 250 1960 799--801. MR0119041 (22 #9808)
  7. Chow, Yuan Shih; Teicher, Henry. Probability theory. Independence, interchangeability, martingales. Third edition. Springer Texts in Statistics. Springer-Verlag, New York, 1997. xxii+488 pp. ISBN: 0-387-98228-0 MR1476912 (98e:60003)
  8. Davies, Laurie. A theorem of Deny with applications to characterization problems. Analytical methods in probability theory (Oberwolfach, 1980), pp. 35--41, Lecture Notes in Math., 861, Springer, Berlin-New York, 1981. MR0655258 (84h:62024)
  9. Davies, Laurie; Shimizu, Ryoichi. On identically distributed linear statistics. Ann. Inst. Statist. Math. 28 (1976), no. 3, 469--489. MR0431467 (55 #4465)
  10. Dufresne, Daniel. The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuar. J. 1990, no. 1-2, 39--79. MR1129194 (92i:62195)
  11. Durrett, Richard; Liggett, Thomas M. Fixed points of the smoothing transformation. Z. Wahrsch. Verw. Gebiete 64 (1983), no. 3, 275--301. MR0716487 (85e:60059)
  12. Embrechts, Paul; Goldie, Charles M. Perpetuities and random equations. Asymptotic statistics (Prague, 1993), 75--86, Contrib. Statist., Physica, Heidelberg, 1994. MR1311930 (95m:60093)
  13. Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403 (42 #5292)
  14. Gnedenko, B. W.; Kolmogorov, A. N. Grenzverteilungen von Summen unabhängiger Zufallsgrössen. (German) Wissenschaftliche Bearbeitung der deutschen Ausgabe: Prof. Dr. Josef Heinhold. Mathematische Lehrbücher und Monographien, II. Abt., Bd. IX Akademie-Verlag, Berlin 1959 viii+279 pp. MR0107295 (21 #6020)
  15. Graf, Siegfried. Statistically self-similar fractals. Probab. Theory Related Fields 74 (1987), no. 3, 357--392. MR0873885 (88c:60038)
  16. Guivarc'h, Yves. Sur une extension de la notion de loi semi-stable. (French) [On an extension of the notion of semistable law] Ann. Inst. H. Poincaré Probab. Statist. 26 (1990), no. 2, 261--285. MR1063751 (91i:60141)
  17. Johansen, S. An application of extreme point methods to the representation of infinitely divisible distributions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 5 1966 304--316. MR0203765 (34 #3613)
  18. Kahane, J.-P.; Peyrière, J. Sur certaines martingales de Benoit Mandelbrot. Advances in Math. 22 (1976), no. 2, 131--145. MR0431355 (55 #4355)
  19. Kesten, Harry. Random difference equations and renewal theory for products of random matrices. Acta Math. 131 (1973), 207--248. MR0440724 (55 #13595)
  20. Khintchine, A. Zur Theorie der unbeschränkt teilbaren Verteilungsgesetze. (German) {it Rec. Math. Moscou, n. Ser.} 2 (1937), 79-117. Zbl0016.4100
  21. Liu, Quansheng. Sur une équation fonctionnelle et ses applications: une extension du théorème de Kesten-Stigum concernant des processus de branchement. (French) [On a functional equation and its applications: an extension of the Kesten-Stigum theorem on branching processes] Adv. in Appl. Probab. 29 (1997), no. 2, 353--373. MR1450934 (98j:60124)
  22. Liu, Quansheng. Fixed points of a generalized smoothing transformation and applications to the branching random walk. Adv. in Appl. Probab. 30 (1998), no. 1, 85--112. MR1618888 (99f:60151)
  23. Mandelbrot, Benoit. Multiplications aléatoires itérées et distributions invariantes par moyenne pondérée aléatoire. C. R. Acad. Sci. Paris Sér. A 278 (1974), 289--292. MR0431351 (55 #4352a)
  24. Rachev, S. T.; Rüschendorf, L. Probability metrics and recursive algorithms. Adv. in Appl. Probab. 27 (1995), no. 3, 770--799. MR1341885 (96m:60005)
  25. Ramachandran, B.; Lau, Ka-Sing; Gu, Hua Min. On characteristic functions satisfying a functional equation and related classes of simultaneous integral equations. Sankhy=a Ser. A 50 (1988), no. 2, 190--198. MR1056443 (91g:60023)
  26. Rösler, Uwe. A limit theorem for "Quicksort". RAIRO Inform. Théor. Appl. 25 (1991), no. 1, 85--100. MR1104413 (92f:68028)
  27. Rösler, Uwe. A fixed point theorem for distributions. Stochastic Process. Appl. 42 (1992), no. 2, 195--214. MR1176497 (93k:60038)
  28. Rösler, Uwe. The weighted branching process. Dynamics of complex and irregular systems (Bielefeld, 1991), 154--165, Bielefeld Encount. Math. Phys., VIII, World Sci. Publishing, River Edge, NJ, 1993. MR1340440 (96f:60148)
  29. Rösler, Uwe. A fixed point equation for distributions. Report No. 98-7, Univ. Kiel (1998). Math. Review number not available.
  30. Rösler, U.; Rüschendorf, L. The contraction method for recursive algorithms. Average-case analysis of algorithms (Princeton, NJ, 1998). Algorithmica 29 (2001), no. 1-2, 3--33. MR1887296 (2003c:68096)
  31. Shimizu, Ryoichi. Solution to a functional equation and its application to some characterization problems. Sankhy=a Ser. A 40 (1978), no. 4, 319--332. MR0589287 (81j:60021)

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