J. Beran, Y. Feng, S. Ghosh, and R. Kulik, Long-memory processes, Probabilistic properties and statistical methods, 2013.

J. Bertoin, Subordinators: examples and applications. In Lectures on probability theory and statistics (Saint-Flour, Lecture Notes in Math, vol.1717, pp.1-91, 1997.
DOI : 10.1007/978-3-540-48115-7_1

URL : http://www.zora.uzh.ch/id/eprint/79481/1/M2-Bertoin-subordinateurs.pdf

P. Billingsley, Convergence of probability measures Wiley Series in Probability and Statistics: Probability and Statistics, 1999.

S. Boucheron, G. Lugosi, and P. Massart, Concentration inequalities A nonasymptotic theory of independence, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00794821

L. De-haan, A Spectral Representation for Max-stable Processes, The Annals of Probability, vol.12, issue.4, pp.1194-1204, 1984.
DOI : 10.1214/aop/1176993148

L. De-haan and A. Ferreira, Extreme value theory. Springer Series in Operations Research and Financial Engineering, 2006.

D. Denneberg, Non-additive measure and integral, volume 27 of Theory and Decision Library. Series B: Mathematical and Statistical Methods, 1994.

C. Dombry and Z. Kabluchko, Ergodic decompositions of stationary max-stable processes in terms of their spectral functions. Stochastic Process, Appl, vol.127, issue.6, pp.1763-1784, 2017.

O. Durieu, G. Samorodnitsky, W. , and Y. , From infinite urn schemes to selfsimilar stable processes. Submitted, available at https, 2017.
DOI : 10.1214/16-ejp4492

URL : https://hal.archives-ouvertes.fr/hal-01622790

O. Durieu and Y. Wang, From infinite urn schemes to decompositions of self-similar Gaussian processes, Electronic Journal of Probability, vol.21, issue.23, 2016.
DOI : 10.1214/16-EJP4492

URL : https://hal.archives-ouvertes.fr/hal-01184411

M. Dwass, Extremal Processes, The Annals of Mathematical Statistics, vol.35, issue.4, pp.1718-1725, 1964.
DOI : 10.1214/aoms/1177700394

A. Gnedin, B. Hansen, and J. Pitman, 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

T. Hsing, J. Hüsler, and M. R. Leadbetter, On the exceedance point process for a stationary sequence, Probability Theory and Related Fields, vol.4, issue.1, pp.97-112, 1988.
DOI : 10.1007/BF00718038

Z. Kabluchko, Spectral representations of sum- and max-stable processes, Extremes, vol.97, issue.4, pp.401-424, 2009.
DOI : 10.1007/BFb0087958

URL : https://link.springer.com/content/pdf/10.1007%2Fs10687-009-0083-9.pdf

Z. Kabluchko and M. Schlather, Ergodic properties of max-infinitely divisible processes. Stochastic Process, Appl, vol.120, issue.3, pp.281-295, 2010.
DOI : 10.1016/j.spa.2009.12.002

URL : https://doi.org/10.1016/j.spa.2009.12.002

S. Karlin, 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

URL : http://www.iumj.indiana.edu/IUMJ/FTDLOAD/1968/17/17020/pdf

C. Lacaux and G. Samorodnitsky, Time-changed extremal process as a random sup measure, Bernoulli, vol.22, issue.4, pp.1979-2000, 2016.
DOI : 10.3150/15-BEJ717

URL : https://hal.archives-ouvertes.fr/hal-01102343

J. Lamperti, Semi-stable stochastic processes, Transactions of the American Mathematical Society, vol.104, issue.1, pp.62-78, 1962.
DOI : 10.1090/S0002-9947-1962-0138128-7

J. Lamperti, On Extreme Order Statistics, The Annals of Mathematical Statistics, vol.35, issue.4, pp.1726-1737, 1964.
DOI : 10.1214/aoms/1177700395

URL : http://doi.org/10.1214/aoms/1177700395

M. R. Leadbetter, G. Lindgren, R. , and H. , Extremes and related properties of random sequences and processes, 1983.
DOI : 10.1007/978-1-4612-5449-2

R. Lepage, M. Woodroofe, and J. Zinn, Convergence to a Stable Distribution Via Order Statistics, The Annals of Probability, vol.9, issue.4, pp.624-632, 1981.
DOI : 10.1214/aop/1176994367

I. Molchanov, Theory of random sets. Probability and its Applications, 2005.
DOI : 10.1007/978-1-4471-7349-6

I. Molchanov and K. Strokorb, Max-stable random sup-measures with comonotonic tail dependence. Stochastic Process, Appl, vol.126, issue.9, pp.2835-2859, 2016.
DOI : 10.1016/j.spa.2016.03.004

URL : http://arxiv.org/pdf/1507.03476

O. 'brien, G. L. Torfs, P. J. Vervaat, and W. , Stationary self-similar extremal processes, Probability Theory and Related Fields, vol.12, issue.2, pp.97-119, 1990.
DOI : 10.1007/978-1-4615-8162-8_22

T. Owada and G. Samorodnitsky, Maxima of long memory stationary symmetric $\alpha$-stable processes, and self-similar processes with stationary max-increments, Bernoulli, vol.21, issue.3, pp.1575-1599, 2015.
DOI : 10.3150/14-BEJ614

V. Pipiras and M. Taqqu, Long-range dependence and self-similarity, 2017.
DOI : 10.1017/CBO9781139600347

J. Pitman, Combinatorial stochastic processes, volume 1875 of Lecture Notes in Mathematics, Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, 2002.

S. I. Resnick, Extreme values, regular variation, and point processes, of Applied Probability. A Series of the Applied Probability Trust, 1987.
DOI : 10.1007/978-0-387-75953-1

G. Samorodnitsky, Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes, The Annals of Probability, vol.32, issue.2, pp.1438-1468, 2004.
DOI : 10.1214/009117904000000261

G. Samorodnitsky, Stochastic processes and long range dependence, 2016.
DOI : 10.1007/978-3-319-45575-4

G. Samorodnitsky and Y. Wang, Extremal theory for long range dependent infinitely divisible processes. Submitted, available at https, 2017.

S. A. Stoev, On the ergodicity and mixing of max-stable processes. Stochastic Process, Appl, vol.118, issue.9, pp.1679-1705, 2008.

S. A. Stoev and M. S. Taqqu, Extremal stochastic integrals: a parallel between max-stable processes and ??-stable processes, Extremes, vol.41, issue.4, pp.237-266, 2005.
DOI : 10.1007/978-0-387-75953-1

W. Vervaat, Random upper semicontinuous functions and extremal processes, Probability and lattices, pp.1-56, 1997.