## Electronic Communications in Probability

### Weak convergence of the number of zero increments in the random walk with barrier

We continue the line of research of random walks with a barrier initiated by Iksanov and Möhle (2008). Assuming that the tail of the step of the underlying random walk has a power-like behavior at infinity with the exponent $-\alpha$, $\alpha\in. #### Article information Source Electron. Commun. Probab., Volume 19 (2014), paper no. 74, 11 pp. Dates Accepted: 31 October 2014 First available in Project Euclid: 7 June 2016 Permanent link to this document https://projecteuclid.org/euclid.ecp/1465316776 Digital Object Identifier doi:10.1214/ECP.v19-3641 Mathematical Reviews number (MathSciNet) MR3274520 Zentralblatt MATH identifier 1320.60110 Subjects Primary: 60C05: Combinatorial probability Secondary: 60G09: Exchangeability Rights This work is licensed under a Creative Commons Attribution 3.0 License. #### Citation Marynych, Alexander; Verovkin, Glib. Weak convergence of the number of zero increments in the random walk with barrier. Electron. Commun. Probab. 19 (2014), paper no. 74, 11 pp. doi:10.1214/ECP.v19-3641. https://projecteuclid.org/euclid.ecp/1465316776 #### References • Anderson, Kevin K.; Athreya, Krishna B. A renewal theorem in the infinite mean case. Ann. Probab. 15 (1987), no. 1, 388–393. • de Bruijn, N. G.; ErdÃ¶s, P. On a recursion formula and on some Tauberian theorems. J. Research Nat. Bur. Standards 50, (1953). 161–164. • Dynkin, E. B. Some limit theorems for sums of independent random variables with infinite mathematical expectations. 1961 Select. Transl. Math. Statist. and Probability, Vol. 1 pp. 171–189 Inst. Math. Statist. and Amer. Math. Soc., Providence, R.I. • Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. • Garsia, Adriano; Lamperti, John. A discrete renewal theorem with infinite mean. Comment. Math. Helv. 37 1962/1963 221–234. • Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander. On$\Lambda\$-coalescents with dust component. J. Appl. Probab. 48 (2011), no. 4, 1133–1151.
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