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Central limit theorem for stationary products of toral automorphisms
1. | IRMAR, UMR CNRS 6625, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France, France, France |
References:
[1] |
C. Aistleitner and I. Berkes, On the central limit theorem for $f(n_k x)$, Probab. Theory Related Fields, 146 (2010), 267-289. |
[2] |
A. Ayyer and M. Stenlund, Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms, Chaos, 17 (2007), 043116, 7 pp. |
[3] |
A. Ayyer, C. Liverani and M. Stenlund, Quenched CLT for random toral automorphism, Discrete Contin. Dyn. Syst., 24 (2009), 331-348.
doi: 10.3934/dcds.2009.24.331. |
[4] |
V. I. Bakhtin, Random processes generated by a hyperbolic sequence of mappings (I, II), Rus. Ac. Sci. Izv. Math., 44 (1995), 247-279 and 617-627, (MR1286845). |
[5] |
I. Berkes, On the asymptotic behaviour of $Sf(n_kx)$. Main theorems, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 34 (1976), 319-345.
doi: 10.1007/BF00535967. |
[6] |
B. M. Brown, Martingale central limit theorems, Annals of Math. Statistics, 42 (1971), 59-66. |
[7] |
J.-P. Conze and S. Le Borgne, Limit law for some modified ergodic sums, Stochastics and Dynamics, 11 (2011), 107-133.
doi: 10.1142/S021949371100319X. |
[8] |
J.-P. Conze and S. Le Borgne, Théorème limite central presque sûr pour les marches aléatoires avec trou spectral, [Quenched central limit theorem for random walks with a spectral gap], CRAS, 2011. |
[9] |
J.-P. Conze and A. Raugi, Limit theorems for sequential expanding dynamical systems on [0,1], in "Ergodic Theory and Related Fields," Contemporary Mathematics, 430, Amer. Math. Soc., Providence, RI, (2007), 89-121. |
[10] |
W. Feller, "An Introduction to Probability Theory and its Applications," Vol. II, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971. |
[11] |
V. F. Gaposhkin, Lacunary series and independent functions, (Russian), Uspehi Mat. Nauk, 21 (1966), 3-82. |
[12] |
J. Komlós, A central limit theorem for multiplicative systems, Canad. Math. Bull., 16 (1973), 67-73.
doi: 10.4153/CMB-1973-014-3. |
[13] |
V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210. |
[14] |
B. Petit, Le théorème limite central pour des sommes de Riesz-Raĭkov, Probab. Theory Related Fields, 93 (1992), 407-438.
doi: 10.1007/BF01192715. |
[15] |
L. Polterovich and Z. Rudnick, Stable mixing for cat maps and quasi-morphisms of the modular group, Ergodic Theory Dynam. Systems, 24 (2004), 609-619.
doi: 10.1017/S0143385703000531. |
[16] |
A. Raugi, "Théorème Ergodique Multiplicatif, Produits de Matrices Aléatoires Indépendantes," Publ. Inst. Rech. Math. Rennes, 1996/1997, Univ. Rennes I, Rennes, 1997. |
[17] |
M. Viana, "Stochastic Dynamics of Deterministic Systems," Brazilian Math. Colloquium, IMPA, 1997. |
show all references
References:
[1] |
C. Aistleitner and I. Berkes, On the central limit theorem for $f(n_k x)$, Probab. Theory Related Fields, 146 (2010), 267-289. |
[2] |
A. Ayyer and M. Stenlund, Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms, Chaos, 17 (2007), 043116, 7 pp. |
[3] |
A. Ayyer, C. Liverani and M. Stenlund, Quenched CLT for random toral automorphism, Discrete Contin. Dyn. Syst., 24 (2009), 331-348.
doi: 10.3934/dcds.2009.24.331. |
[4] |
V. I. Bakhtin, Random processes generated by a hyperbolic sequence of mappings (I, II), Rus. Ac. Sci. Izv. Math., 44 (1995), 247-279 and 617-627, (MR1286845). |
[5] |
I. Berkes, On the asymptotic behaviour of $Sf(n_kx)$. Main theorems, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 34 (1976), 319-345.
doi: 10.1007/BF00535967. |
[6] |
B. M. Brown, Martingale central limit theorems, Annals of Math. Statistics, 42 (1971), 59-66. |
[7] |
J.-P. Conze and S. Le Borgne, Limit law for some modified ergodic sums, Stochastics and Dynamics, 11 (2011), 107-133.
doi: 10.1142/S021949371100319X. |
[8] |
J.-P. Conze and S. Le Borgne, Théorème limite central presque sûr pour les marches aléatoires avec trou spectral, [Quenched central limit theorem for random walks with a spectral gap], CRAS, 2011. |
[9] |
J.-P. Conze and A. Raugi, Limit theorems for sequential expanding dynamical systems on [0,1], in "Ergodic Theory and Related Fields," Contemporary Mathematics, 430, Amer. Math. Soc., Providence, RI, (2007), 89-121. |
[10] |
W. Feller, "An Introduction to Probability Theory and its Applications," Vol. II, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971. |
[11] |
V. F. Gaposhkin, Lacunary series and independent functions, (Russian), Uspehi Mat. Nauk, 21 (1966), 3-82. |
[12] |
J. Komlós, A central limit theorem for multiplicative systems, Canad. Math. Bull., 16 (1973), 67-73.
doi: 10.4153/CMB-1973-014-3. |
[13] |
V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210. |
[14] |
B. Petit, Le théorème limite central pour des sommes de Riesz-Raĭkov, Probab. Theory Related Fields, 93 (1992), 407-438.
doi: 10.1007/BF01192715. |
[15] |
L. Polterovich and Z. Rudnick, Stable mixing for cat maps and quasi-morphisms of the modular group, Ergodic Theory Dynam. Systems, 24 (2004), 609-619.
doi: 10.1017/S0143385703000531. |
[16] |
A. Raugi, "Théorème Ergodique Multiplicatif, Produits de Matrices Aléatoires Indépendantes," Publ. Inst. Rech. Math. Rennes, 1996/1997, Univ. Rennes I, Rennes, 1997. |
[17] |
M. Viana, "Stochastic Dynamics of Deterministic Systems," Brazilian Math. Colloquium, IMPA, 1997. |
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