Download this PDF file Fullscreen Fullscreen Off
References
- Barbour, A. D.; Gnedin, A. V. Regenerative compositions in the case of slow variation. Stochastic Process. Appl. 116 (2006), no. 7, 1012--1047. MR2238612
- Billingsley, Patrick. Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396
- Bingham, N. H. Limit theorems for regenerative phenomena, recurrent events and renewal theory. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 21 (1972), 20--44. MR0353459
- Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1989. xx+494 pp. ISBN: 0-521-37943-1 MR1015093
- Durrett, Richard; Liggett, Thomas M. Fixed points of the smoothing transformation. Z. Wahrsch. Verw. Gebiete 64 (1983), no. 3, 275--301. MR0716487
- Gnedin, Alexander V. The Bernoulli sieve. Bernoulli 10 (2004), no. 1, 79--96. MR2044594
- Gnedin, Alexander V. Regeneration in random combinatorial structures. Probab. Surv. 7 (2010), 105--156. MR2684164
- Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander. Limit theorems for the number of occupied boxes in the Bernoulli sieve. Theory Stoch. Process. 16 (2010), no. 2, 44--57. MR2777900
- Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander. The Bernoulli sieve: an overview. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 329--341, Discrete Math. Theor. Comput. Sci. Proc., AM, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2010. MR2735350
- Gnedin, Alexander V.; Iksanov, Alexander M.; Negadajlov, Pavlo; Rösler, Uwe. The Bernoulli sieve revisited. Ann. Appl. Probab. 19 (2009), no. 4, 1634--1655. MR2538083
- Gnedin, Alexander; Pitman, Jim. Regenerative composition structures. Ann. Probab. 33 (2005), no. 2, 445--479. MR2122798
- Gnedin, Alexander; Pitman, Jim; Yor, Marc. Asymptotic laws for regenerative compositions: gamma subordinators and the like. Probab. Theory Related Fields 135 (2006), no. 4, 576--602. MR2240701
- Gnedin, Alexander; Pitman, Jim; Yor, Marc. Asymptotic laws for compositions derived from transformed subordinators. Ann. Probab. 34 (2006), no. 2, 468--492. MR2223948
- Iksanov, Alexander. On the number of empty boxes in the Bernoulli sieve II. Stochastic Process. Appl. 122 (2012), no. 7, 2701--2729. MR2926172
- Iksanov, A.: Functional limit theorems for renewal shot noise processes, ARXIV1202.1950
- Iksanov, A., Marynych, A. and Meiners, M.: Moment convergence in renewal theory, ARXIV1208.3964
- Sgibnev, M. S. On the renewal theorem in the case of infinite variance. (Russian) Sibirsk. Mat. Zh. 22 (1981), no. 5, 178--189, 224. MR0632826
- Walker, Stephen; Muliere, Pietro. A characterization of a neutral to the right prior via an extension of Johnson's sufficientness postulate. Ann. Statist. 27 (1999), no. 2, 589--599. MR1714716
- 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

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