Publications

Book

V. Lucarini, D. Faranda, A. C. M. Freitas, J. M. Freitas, M. Holland, T. Kuna, M. Nicol, and S. Vaienti. Extremes and Recurrence in Dynamical Systems. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley, Hoboken, NJ, 2016.

Extremes

Published papers and preprints

  1. C. Correia, A.C.M. Freitas, J.M. Freitas, Cluster distributions for dynamically defined point processes, Preprint 2022, CMUP[2022-35].

  2. A.C.M. Freitas, J.M. Freitas, M. Todd, Enriched functional limit theorems for dynamical systems, Preprint 2020, arXiv:2011.10153.

  3. A.C.M. Freitas, J.M. Freitas, J.V. Soares, Rare events for product fractal sets, J. Phys. A: Math. Theor., 54, no. 34, 345202, 2021.

  4. A.C.M. Freitas, J.M. Freitas, M. Magalhães, S. Vaienti, Point processes of non stationary sequences generated by sequential and random dynamical systems, J. Stat. Phys., 181, no.4, 1365-1409, 2020.

  5. A.C.M. Freitas, J.M. Freitas, F.B. Rodrigues, J.V. Soares, Rare events for Cantor target sets, Comm. Math. Phys., 378, no. 1, 75-115, 2020.

  6. M. Abadi, A.C.M. Freitas, J.M. Freitas, Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution, J. London Math. Soc., 102, no.2, 670-694, 2020.

  7. A.C.M. Freitas, J.M. Freitas, and M. Magalhães. Complete convergence and records for dynamically generated stochastic processes, Trans. Amer. Math. Soc., 373, no. 1, 435–478, 2020.

  8. M. Abadi, A.C.M. Freitas, J.M. Freitas, Clustering indices and decay of correlations in non-Markovian models, Nonlinearity, 32, no. 12, 4853-4870, 2019.

  9. A.C.M. Freitas, J.M. Freitas, M. Magalhães, Convergence of Marked Point Processes of Excesses for Dynamical Systems, J. Eur. Math. Soc. (JEMS), 20, no. 9, 2131–2179, 2018.

  10. A.C.M. Freitas, J.M. Freitas, S. Vaienti, Extreme Value Laws for sequences of intermittent maps, Proc. Amer. Math. Soc., 146, no. 5, 2103–2116, 2018.

  11. A.C.M. Freitas, J.M. Freitas, S. Vaienti, Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems, Ann. Inst. Henri Poincaré Probab. Stat., 53, no. 3, 1341–1370, 2017.

  12. D. Azevedo, A.C.M. Freitas, J.M. Freitas, F.B. Rodrigues, Extreme Value Laws for dynamical systems with countable extremal sets, J. Stat. Phys., 167, no. 5, 1244–1261, 2017.

  13. A.C.M. Freitas, J.M. Freitas, M. Todd, S. Vaienti, Rare Events for the Manneville-Pomeau map, Stochastic Process. Appl., 126, no. 11, 3463–3479, 2016.

  14. M. Brito, A. C. M. Freitas, and J. M. Freitas. Tail prepivoting for the hill estimator, J. Phys. A: Math. Theor., 49, no. 19, 194004, 2016.

  15. M. Brito, L. Cavalcante, A.C.M. Freitas, Bias corrected geometric-type estimators of the tail index, J. Phys. A: Math. Theor., 49, no. 21, 214003, 2016.

  16. D. Azevedo, A.C.M. Freitas, J.M. Freitas, F.B. Rodrigues, Clustering of extreme events created by multiple correlated maxima, Phys. D, 315, 33–48, 2016.

  17. M. Carvalho, A. C. M. Freitas, J. M. Freitas, M. Holland, and M. Nicol. Extremal dichotomy for uniformly hyperbolic systems. Dyn. Syst., 30, no. 4, 383–403, 2015.

  18. M. Brito, L. Cavalcante, A.C.M. Freitas, Modelling of extremal earthquakes, Mathematics of Energy and Climate Change, 39–60, 2015.

  19. A. C. M. Freitas, J. M. Freitas, and M. Todd. Speed of convergence for laws of rare events and escape rates, Stochastic Process. Appl., 125, no. 4, 1653–1687, 2015.

  20. A.C.M. Freitas, Asymptotic distribution of the maximum for a chaotic economic model, Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications, 193–201, 2013.

  21. A.C.M. Freitas, J.M. Freitas, M. Todd, The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics, Comm. Math. Phys., 321, no. 2, 483-527, 2013.

  22. A.C.M. Freitas, J.M. Freitas, M. Todd, Extremal Index, Hitting Time Statistics and periodicity, Adv. Math., 231, no. 5, 2626-2665, 2012.

  23. A.C.M. Freitas, J.M. Freitas, M. Todd, Extreme Value Laws in Dynamical Systems for Non-smooth Observations, J. Stat. Phys., 142, no. 1, 108-126, 2011.

  24. A.C.M. Freitas, J.M. Freitas, M. Todd, Statistical properties of the maximum for non-uniformly hyperbolic dynamics, Dynamics, Games and Science I, 365-374, Springer, Heidelberg, 2011.

  25. M. Brito, A.C.M. Freitas, Consistent estimation of the tail index for dependent data, Stat. Probab. Lett., 80, no. 23-24, 1835-1843, 2010.

  26. A.C.M. Freitas, J.M. Freitas, M. Todd, Hitting Time Statistics and Extreme Value Theory, Probab. Theory Related Fields, 147, no. 3, 675-710, 2010.

  27. A.C.M. Freitas, Statistics of the maximum for the tent map, Chaos Solitons Fractals, 42, no. 1, 604-608, 2009.

  28. M. Brito, A.C.M. Freitas, Edgeworth expansion for an estimator of the adjustment coefficient, Insurance Math. Econom., 43, no. 2, 203-208, 2008.

  29. A.C.M. Freitas, J.M. Freitas, Extreme Values for Benedicks-Carleson quadratic maps, Ergodic Theory Dynam. Systems, 28, no. 4, 1117-1133, 2008.

  30. A.C.M. Freitas, J.M. Freitas, On the link between dependence and independence in extreme value theory for dynamical systems, Stat. Probab. Lett., 78, no.9, 1088-1093, 2008.

  31. M. Brito, A.C.M. Freitas, Weak convergence of a bootstrap geometric-type estimator with applications to risk theory, Insurance Math. Econom., 38, no.3, 571-584, 2006.

  32. M. Brito, A.C.M. Freitas, Limiting behaviour of a geometric-type estimator for tail indices, Insurance Math. Econom. 33, no. 2, 211-226, 2003.

Book chapters

A.C.M. Freitas, J.M. Freitas, Quantificar o acaso, in “13 Viagens pelo Mundo da Matemática”, edited by C. Sá and J. Rocha, chapter 13, Universidade do Porto (2010).

Papers in conference proceedings

  1. M. Brito, A.C.M. Freitas, On the consistency of the geometric-type estimator for the tail Pareto index. Bulletin of the International Statistical Institute - 56th Session, 2007.

  2. M. Brito, A.C.M. Freitas, Limites de confiança bootstrap para o coeficiente de ajustamento. Em: Ciência Estatística (eds L. Castro, E. Martins, C. Rocha, M. F. Oliveira, M. Leal e F. Rosado), Edições SPE, 205-215, 2006.

  3. M. Brito, A.C.M. Freitas, Intervalos de confiança assimptóticos para o coeficiente de ajustamento na teoria do risco. Em: Literacia e Estatística (eds P. Brito, A. Figueiredo, F. Sousa, P. Teles e F. Rosado), Edições SPE, 167-176, 2003.

  4. M. Brito, A.C.M. Freitas, Estimação do Coeficiente de Cauda Exponencial. Em: Um Olhar sobre a Estatística (eds P. Oliveira e E. Athayde), Edições SPE, 223-237, 2001.

Theses

Estimação do Coeficiente de Cauda Exponencial. Aplicação à Teoria do Risco, Ph.D. Thesis, Universidade do Porto, 2006.

Estimação do Coeficiente de Cauda Exponencial, MSc. Thesis, Universidade do Porto, 1999.