K-limit laws of return and hitting times

Discrete and Continuous Dynamical Systems

Volumn 15, Issue 1, 2006, Pages 73-86

  Chaumoitre V ^a   Kupsa, M ^b  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Hitting times; K limit law; Rank one; Return times

Indexed keywords

EID: 33745278892     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.15.73     Document Type: Article

References (22)

1. M. Abadi, Statistics and error terms of occurrence times in mixing processes, preprint (2003) (mp-arc preprint).
2. M. Abadi, Sharp error terms and necessary conditions for exponential hitting times in mixing processes, Ann. Probab. 32 (2004), no1A, pp.243-264.
3. M. Abadi, Exponential approximation for hitting times in mixing processes, Math. Phys. Electron. J. 7 (2001), Paper 2, 19pp. (electronic).
4. M. Abadi, A. Galves, Inequalities for the occurrences times of rare events in mixing processes. The state of art. Inhomogeneous random systems (Cergy-Pontoise, 2000), Markov Process. Related Fields 7 (2001), no1, pp.97-112.
5. X. Bressaud, R. Zweimuller, Non exponential law of entrance times in asymptotically rare events for intermittent maps with infinite invariant measure, Ann. Henri Poincaré 2 (2001), no3, pp.501-512.
6. R.V. Chacon, Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc. 22 (1969), pp.559-562.
7. V. Chaumoître and M. Kupsa Asympotics for return times of rank-one systems, Stochastics and Dynamics 5 (2005) no1, pp.65-73.
8. Z. Coelho, Asymptotic laws for symbolic dynamical systems, Proceedings of the Conference held in Temuco, 1997, London Math. Soc. Lecture Note Ser. 279, Cambridge University Press, (2000), pp. 123-165.
9. Z. Coelho and E. de Faria, Limit laws for entrance times for homeomorphisms of the circle, Israel J. Math. 93 (1996), pp.73-92.
10. M. Denker, M. Gordin, Mikhail, A. Sharova, A Poisson limit theorem for toral automorphisms, Illinois J. Math. 48 (2004), no1, pp. 1-20.
11. F. Durand and A. Maass, Limit laws of entrance times for low-complexity Cantor minimal systems, Nonlinearity 14 (2001), no4, pp.683-700.
12. S. Ferenczi, Systems of finite rank, Colloq. Math. 73 (1997), no1, pp.35-65.
13. A. Galves, B. Schmitt, Inequalities for hitting times in mixing dynamical systems, Random Comput. Dynam. 5 (1997), no4, pp. 337-347.
14. M. Hirata, Poisson law for Axiom A diffeomorphisms, Ergodic Theory Dynam. Systems 13 (1993), no3, pp.533-556.
15. M. Hirata, Poisson law for the dynamical systems with the "self-mixing" conditions, Dynamical Systems and Chaos 1, (Hachioji, 1994), 87-96, World Sci. Publishing, River Edge, NJ, (1995), pp.87-96.
16. N. Haydn, Y. Lacroix and S. Vaienti, Hitting and return times in ergodic dynamical systems, Annals of Probability 33, (2005), no5, pp. 2043-2050.
17. M. Hirata, B. Saussol and S. Vaienti, Statistics of return times: a general framework and new applications, Comm. Math. Phys. 206 (1999), no1, pp.33-55
18. M. Kupsa and Y. Lacroix, Asymptotics for hitting times, Annals of Probability 33, no2 (2005), pp.610-619.
19. Y. Lacroix, Possible limit laws for entrance times of an ergodic aperiodic dynamical system, Israel J. Math. 132 (2002), pp.253-264.
20. X. Méla and K. Petersen, Dynamical properties of the Pascal adic transformation, Ergodic Theory Dynam. Systems 25 (2005), no1, pp.227-256.
21. B. Pitskel, Poisson limit law for Markov chains, Ergodic Theory Dynam. Systems 11 (1991), no3, pp.501-513.
22. B. Saussol, " Etude statistique de systèmes dynamiques dilatants", PhD thesis, Toulon, France, 1998.