메뉴 건너뛰기




Volumn 151, Issue 3-4, 2011, Pages 705-734

Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps

Author keywords

[No Author keywords available]

Indexed keywords


EID: 80455140222     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-010-0312-9     Document Type: Article
Times cited : (58)

References (33)
  • 1
    • 33644599162 scopus 로고    scopus 로고
    • Limit theorems in the stadium billard
    • Bálint P., Gouëzel S.: Limit theorems in the stadium billard. Commuun. Math. Phys. 263, 451-512 (2006).
    • (2006) Commuun. Math. Phys. , vol.263 , pp. 451-512
    • Bálint, P.1    Gouëzel, S.2
  • 2
    • 0032395342 scopus 로고    scopus 로고
    • A central limit theorem for contractive stochastic dynamical systems
    • Benda M.: A central limit theorem for contractive stochastic dynamical systems. J. Appl. Probab. 35, 200-205 (1998).
    • (1998) J. Appl. Probab. , vol.35 , pp. 200-205
    • Benda, M.1
  • 3
    • 0035564935 scopus 로고    scopus 로고
    • The tail of the stationary distribution of an autoregressive process with ARCH(1) errors
    • Borkovec M., Klüppelberg C.: The tail of the stationary distribution of an autoregressive process with ARCH(1) errors. Ann. Appl. Probab. 11(4), 1220-1241 (2001).
    • (2001) Ann. Appl. Probab. , vol.11 , Issue.4 , pp. 1220-1241
    • Borkovec, M.1    Klüppelberg, C.2
  • 4
    • 79953690609 scopus 로고    scopus 로고
    • Convergence to stable laws for a class multidimensional stochastic recursions
    • (accepted)
    • Buraczewski, D., Damek, E., Guivarc'h, Y.: Convergence to stable laws for a class multidimensional stochastic recursions. Probab. Theory Relat. Fields (2009, accepted).
    • (2009) Probab. Theory Relat. Fields
    • Buraczewski, D.1    Damek, E.2    Guivarc'h, Y.3
  • 6
    • 0002284829 scopus 로고    scopus 로고
    • Iterated random functions
    • Diaconis P., Freedman D.: Iterated random functions. SIAM Rev. 41(1), 45-76 (1999).
    • (1999) SIAM Rev. , vol.41 , Issue.1 , pp. 45-76
    • Diaconis, P.1    Freedman, D.2
  • 7
    • 0000732230 scopus 로고
    • Implicit renewal theory and tails of solutions of random equations
    • Goldie Ch. M.: Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1(1), 126-166 (1991).
    • (1991) Ann. Appl. Probab. , vol.1 , Issue.1 , pp. 126-166
    • Goldie, C.M.1
  • 10
    • 0040176238 scopus 로고
    • Regular variation in the tail behaviour of solutions of random difference equations
    • Grey D. R.: Regular variation in the tail behaviour of solutions of random difference equations. Ann. Appl. Probab. 4(1), 169-183 (1994).
    • (1994) Ann. Appl. Probab. , vol.4 , Issue.1 , pp. 169-183
    • Grey, D.R.1
  • 11
    • 0012486329 scopus 로고
    • On limit distribution for a random walk on the line
    • Grincevičius A. K.: On limit distribution for a random walk on the line. Lithuanian Math. J. 15, 580-589 (1975).
    • (1975) Lithuanian Math. J. , vol.15 , pp. 580-589
    • Grincevičius, A.K.1
  • 12
    • 0002226905 scopus 로고
    • Products of random affine transformations
    • Grincevičius A. K.: Products of random affine transformations. Lithuanian Math. J. 20, 279-282 (1980).
    • (1980) Lithuanian Math. J. , vol.20 , pp. 279-282
    • Grincevičius, A.K.1
  • 13
    • 2942652352 scopus 로고
    • Extension d'un théorèm de Choquet-Deny à une class de group non abéliens
    • France
    • Guivarc'h, Y.: Extension d'un théorèm de Choquet-Deny à une class de group non abéliens. Astérisque 4 Soc. Math. France, pp. 41-60 (1973).
    • (1973) Astérisque 4 Soc. Math. , pp. 41-60
    • Guivarc'h, Y.1
  • 14
    • 34248558363 scopus 로고    scopus 로고
    • Heavy tail properties of multidimensional stochastic recursions
    • Guivarc'h Y.: Heavy tail properties of multidimensional stochastic recursions. IMS Lect. Notes Monogr. Ser. Dyn. Stoch. 48, 85-99 (2006).
    • (2006) IMS Lect. Notes Monogr. Ser. Dyn. Stoch. , vol.48 , pp. 85-99
    • Guivarc'H, Y.1
  • 15
    • 43449102209 scopus 로고    scopus 로고
    • On spectral properties of a family of transfer operators and convergence to stable laws for affine random walks
    • Guivarc'h Y., Le Page É.: On spectral properties of a family of transfer operators and convergence to stable laws for affine random walks. Ergod. Theory Dyn. Syst. 28, 423-446 (2008).
    • (2008) Ergod. Theory Dyn. Syst. , vol.28 , pp. 423-446
    • Guivarc'H, Y.1    Le Page, E.2
  • 17
    • 84966210686 scopus 로고
    • Sur un théorème spectral et son application aux noyaux lipchitziens
    • Hennion H.: Sur un théorème spectral et son application aux noyaux lipchitziens. Proc. Am. Math. Soc. 118, 627-634 (1993).
    • (1993) Proc. Am. Math. Soc. , vol.118 , pp. 627-634
    • Hennion, H.1
  • 18
    • 4544363612 scopus 로고    scopus 로고
    • Central limit theorems for iterated random Lipschitz mappings
    • Hennion H., Hervé L.: Central limit theorems for iterated random Lipschitz mappings. Ann. Probab. 32(3A), 1934-1984 (2004).
    • (2004) Ann. Probab. , vol.32 , Issue.3 A , pp. 1934-1984
    • Hennion, H.1    Hervé, L.2
  • 19
    • 14544305349 scopus 로고    scopus 로고
    • Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
    • Springer, Berlin
    • Hennion, H., Hervé, L.: Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness. Lecture Notes in Mathematics, vol. 1766. Springer, Berlin (2001).
    • (2001) Lecture Notes in Mathematics , vol.1766
    • Hennion, H.1    Hervé, L.2
  • 20
    • 84862102475 scopus 로고    scopus 로고
    • The Nagaev method via the Keller-Liverani theorem
    • France (accepted)
    • Hervé, L., Pène, F.: The Nagaev method via the Keller-Liverani theorem. Bull. Soc. Math. France (2010, accepted).
    • (2010) Bull. Soc. Math.
    • Hervé, L.1    Pène, F.2
  • 21
    • 0001386063 scopus 로고
    • Theoreme ergodique pour des classes doperations non completement continues
    • Ionescu-Tulcea C. T., Marinescu G.: Theoreme ergodique pour des classes doperations non completement continues. Ann. Math. 52(1), 140-147 (1950).
    • (1950) Ann. Math. , vol.52 , Issue.1 , pp. 140-147
    • Ionescu-Tulcea, C.T.1    Marinescu, G.2
  • 22
    • 73949113905 scopus 로고    scopus 로고
    • Limit theorems for additive functionals of a Markov chain
    • Jara M., Komorowski T., Olla S.: Limit theorems for additive functionals of a Markov chain. Ann. Appl. Probab. 19(6), 2270-2300 (2009).
    • (2009) Ann. Appl. Probab. , vol.19 , Issue.6 , pp. 2270-2300
    • Jara, M.1    Komorowski, T.2    Olla, S.3
  • 24
    • 2942672026 scopus 로고
    • Random difference equations and renewal theory for products of random matrices
    • Kesten H.: Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207-248 (1973).
    • (1973) Acta Math. , vol.131 , pp. 207-248
    • Kesten, H.1
  • 25
    • 0001661229 scopus 로고
    • Renewal theory for functionals of a Markov chain with general state space
    • Kesten H.: Renewal theory for functionals of a Markov chain with general state space. Ann. Probab. 2, 355-386 (1974).
    • (1974) Ann. Probab. , vol.2 , pp. 355-386
    • Kesten, H.1
  • 26
    • 14544302928 scopus 로고
    • Théorèmes de renouvellement pour les produits de matrices aléatoires
    • Séminaires de probabilités Rennes 1983. Publ. Sém. Math. Univ. Rennes
    • Le Page, É.: Théorèmes de renouvellement pour les produits de matrices aléatoires. Équations aux différences aléatoires. Séminaires de probabilités Rennes 1983. Publ. Sém. Math., vol. 1. Univ. Rennes (1983).
    • (1983) Équations aux différences aléatoires , vol.1
    • Le Page, E.1
  • 27
    • 0001702994 scopus 로고
    • A contraction principle for certain Markov chains and its applications
    • (Brunswick, Maine, 1984). Contemporary Mathematic Amer. Math. Soc., Providence, RI
    • Letac, G.: A contraction principle for certain Markov chains and its applications. Random matrices matrices and their applications (Brunswick, Maine, 1984). Contemporary Mathematic, vol. 50. Amer. Math. Soc., Providence, RI, pp. 263-273 (1986).
    • (1986) Random matrices matrices and their applications , vol.50 , pp. 263-273
    • Letac, G.1
  • 28
    • 33748759495 scopus 로고    scopus 로고
    • Invariant measures and their properties. A functional analytic point of view
    • Pubblicazioni della Classe di Scienze, Scuola Normale Superiore, Pisa. Centro di Ricerca Matematica "Ennio De Giorgi": Proceedings. Scuola Normale Superiore, Pisa
    • Liverani, C.: Invariant measures and their properties. A functional analytic point of view. In: Dynamical Systems. Part II: topological Geometrical and Ergodic Properties of Dynamics. Pubblicazioni della Classe di Scienze, Scuola Normale Superiore, Pisa. Centro di Ricerca Matematica "Ennio De Giorgi": Proceedings. Scuola Normale Superiore, Pisa (2004).
    • (2004) Dynamical Systems. Part II: Topological Geometrical and Ergodic Properties of Dynamics
    • Liverani, C.1
  • 29
    • 0034345591 scopus 로고    scopus 로고
    • A central limit theorem for additive functions of a Markov chain
    • Maxwell M., Woodroofe M.: A central limit theorem for additive functions of a Markov chain. Ann. Probab. 28, 713-724 (2000).
    • (2000) Ann. Probab. , vol.28 , pp. 713-724
    • Maxwell, M.1    Woodroofe, M.2
  • 30
    • 0001538561 scopus 로고
    • Some limit theorems for stationary Markov chains
    • Nagaev S. V.: Some limit theorems for stationary Markov chains. Theory Probab. Appl. 11, 378-406 (1957).
    • (1957) Theory Probab. Appl. , vol.11 , pp. 378-406
    • Nagaev, S.V.1
  • 31
    • 4944244483 scopus 로고    scopus 로고
    • A general Choquet-Deny theorem for nilpotent groups
    • Raugi A.: A general Choquet-Deny theorem for nilpotent groups. Ann. Inst. H. Poincaré Probab. Stat. 40, 677-683 (2004).
    • (2004) Ann. Inst. H. Poincaré Probab. Stat. , vol.40 , pp. 677-683
    • Raugi, A.1
  • 32
    • 0001565579 scopus 로고
    • On a stochastic difference equation and a representation of non-negativeve infinitely divisible random variables
    • Vervaat W.: On a stochastic difference equation and a representation of non-negativeve infinitely divisible random variables. Adv. Appl. Prob. 11, 750-783 (1979).
    • (1979) Adv. Appl. Prob. , vol.11 , pp. 750-783
    • Vervaat, W.1
  • 33
    • 0034337857 scopus 로고    scopus 로고
    • A central limit theorem for iterated random functions
    • Woodroofe M., Wu W. B.: A central limit theorem for iterated random functions. J. Appl. Probab. 37, 748-755 (2000).
    • (2000) J. Appl. Probab. , vol.37 , pp. 748-755
    • Woodroofe, M.1    Wu, W.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.