On the number of distinct values in a large sample from an infinite discrete distribution, no. supplement II, pp.67-75, 1960. ,
Convergence of probability measures Wiley Series in Probability and Statistics: Probability and Statistics, p.1700749, 1999. ,
Sub-fractional Brownian motion and its relation to occupation times, Statistics & Probability Letters, vol.69, issue.4, pp.405-419, 2004. ,
DOI : 10.1016/j.spl.2004.06.035
Particle picture interpretation of some Gaussian processes related to fractional Brownian motion, Stochastic Process, Appl, vol.122, issue.5, pp.2134-2154, 2012. ,
Estimating the Number of Species: A Review, Journal of the American Statistical Association, vol.21, issue.421, pp.364-373, 1993. ,
DOI : 10.1080/01621459.1993.10594330
The invariance principle for stationary processes, Teor. Verojatnost. i Primenen, vol.15, pp.498-509, 1970. ,
A series expansion of fractional Brownian motion, Probability Theory and Related Fields, vol.130, issue.1, pp.39-55, 2004. ,
DOI : 10.1007/s00440-003-0310-2
Selfsimilar processes, Princeton Series in Applied Mathematics, p.1920153, 2002. ,
DOI : 10.1515/9781400825103
A simple construction of the fractional Brownian motion, Stochastic Process, Appl, vol.109, issue.2, pp.203-223, 2004. ,
Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws, Probability Surveys, vol.4, issue.0, pp.146-171, 2007. ,
DOI : 10.1214/07-PS092
Power law P??lya???s urn and fractional Brownian motion, Probability Theory and Related Fields, vol.5, issue.3, pp.691-719, 2013. ,
DOI : 10.1007/s00440-012-0468-6
An example of infinite dimensional quasi-helix, Contemp. Math, vol.336, pp.195-201, 2002. ,
DOI : 10.1090/conm/336/06034
Central Limit Theorems for Certain Infinite Urn Schemes, Indiana University Mathematics Journal, vol.17, issue.4, pp.373-401, 1967. ,
DOI : 10.1512/iumj.1968.17.17020
Fractional Brownian motion as a weak limit of Poisson shot noise processes?with applications to finance, Stochastic Process, Appl, vol.113, issue.2, pp.333-351, 2004. ,
Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. Sci. URSS (N.S.), vol.26, pp.115-118, 1940. ,
A decomposition of the bifractional Brownian motion and some applications, Statistics & Probability Letters, vol.79, issue.5, pp.619-624, 2009. ,
DOI : 10.1016/j.spl.2008.10.009
Fractional Brownian motions, fractional noises and applications, SIAM Rev, pp.422-437, 1968. ,
Scaling Limits for Cumulative Input Processes, Mathematics of Operations Research, vol.32, issue.4, pp.890-918, 2007. ,
DOI : 10.1287/moor.1070.0267
On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion, ALEA Lat, Am. J. Probab. Math. Stat, vol.4, pp.245-255, 2008. ,
Long-range dependence and self-similarity, 2016. ,
Combinatorial stochastic processes Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, Lecture Notes in Mathematics, vol.1875, p.2245368, 2002. ,
Problems and theorems in analysis I: Series, integral calculus, theory of functions, p.344042, 1972. ,
A decomposition of sub-fractional Brownian motion, Math. Rep. (Bucur.), vol.11, issue.61 1, pp.67-74, 2009. ,
Long range dependence, Found. Trends Stoch, Syst, vol.1, issue.3, pp.163-257, 2006. ,
Principles of random walk, The University Series in Higher Mathematics, p.171290, 1964. ,
Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, vol.31, pp.287-302, 1975. ,
Weak convergence and empirical processes, With applications to statistics, p.1385671, 1996. ,
The authors would like to thank David Nualart and Gennady Samorodnitsky for helpful discussions. The first author would like to thank the hospitality and financial support from Taft Research Center and Department of Mathematical Sciences at University of Cincinnati, for his visit in, when most of the results were obtained. The first author's research was partially supported by the EJP, paper 43, p.22, 2015. ,
ECP over for-profit journals 1 LOCKSS: Lots of Copies Keep Stuff Safe http://www.lockss.org/ 2 EJMS: Electronic Journal Management System http ,