The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Avram, Florin; Taqqu, Murad S. Weak convergence of sums of moving averages in the $\alpha$-stable domain of attraction. Ann. Probab. 20 (1992), no. 1, 483--503. MR1143432
  • Bartkiewicz, K., Jakubowski, A., Mikosch, Th., Wintenberger, O. (2011). Stable limits for sums of dependent infinite variance random variables. Probab. Theory Relat. Fields./ 150, 337-372.
  • Basrak, B., Krizmanic, D., Segers, J. (2010). A functional limit theorem for partial sums of dependent random variables with infinite variance. To appear in Annals of Probability.
  • Daley, D. J. Stochastically monotone Markov chains. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 10 1968 305--317. MR0242270
  • Diaconis, Persi; Freedman, David. Iterated random functions. SIAM Rev. 41 (1999), no. 1, 45--76. MR1669737
  • Esary, J. D.; Proschan, F.; Walkup, D. W. Association of random variables, with applications. Ann. Math. Statist. 38 1967 1466--1474. MR0217826
  • Goldie, Charles M. Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1 (1991), no. 1, 126--166. MR1097468
  • Letac, Gérard. A contraction principle for certain Markov chains and its applications. Random matrices and their applications (Brunswick, Maine, 1984), 263--273, Contemp. Math., 50, Amer. Math. Soc., Providence, RI, 1986. MR0841098
  • Liggett, Thomas M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231
  • Louhichi, Sana; Rio, Emmanuel. Convergence du processus de sommes partielles vers un processus de Lévy pour les suites associées. (French) [Convergence of partial sum processes to Levy processes for associated sequences] C. R. Math. Acad. Sci. Paris 349 (2011), no. 1-2, 89--91. MR2755704
  • Mirek, M. (2011). Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps. Probab. Theory Relat. Fields./ 151, 705-734.
  • Newman, C. M.; Wright, A. L. An invariance principle for certain dependent sequences. Ann. Probab. 9 (1981), no. 4, 671--675. MR0624694
  • Newman, C. M.; Wright, A. L. Associated random variables and martingale inequalities. Z. Wahrsch. Verw. Gebiete 59 (1982), no. 3, 361--371. MR0721632
  • Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932
  • Sato, Ken-iti. Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4 MR1739520
  • Skorohod, A. V. Limit theorems for stochastic processes. (Russian) Teor. Veroyatnost. i Primenen. 1 (1956), 289--319. MR0084897
  • Tyran-Kamińska, Marta. Weak convergence to Lévy stable processes in dynamical systems. Stoch. Dyn. 10 (2010), no. 2, 263--289. MR2652889
  • Tyran-Kamińska, Marta. Convergence to Lévy stable processes under some weak dependence conditions. Stochastic Process. Appl. 120 (2010), no. 9, 1629--1650. MR2673968
  • Whitt, Ward. Stochastic-process limits. An introduction to stochastic-process limits and their application to queues. Springer Series in Operations Research. Springer-Verlag, New York, 2002. xxiv+602 pp. ISBN: 0-387-95358-2 MR1876437

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.