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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.
|
[2] |
A. Ayyer and M. Stenlund, Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms,, Chaos, 17 (2007).
|
[3] |
A. Ayyer, C. Liverani and M. Stenlund, Quenched CLT for random toral automorphism,, Discrete Contin. Dyn. Syst., 24 (2009), 331.
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.
|
[5] |
I. Berkes, On the asymptotic behaviour of $Sf(n_kx)$. Main theorems,, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 34 (1976), 319.
doi: 10.1007/BF00535967. |
[6] |
B. M. Brown, Martingale central limit theorems,, Annals of Math. Statistics, 42 (1971), 59.
|
[7] |
J.-P. Conze and S. Le Borgne, Limit law for some modified ergodic sums,, Stochastics and Dynamics, 11 (2011), 107.
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). Google Scholar |
[9] |
J.-P. Conze and A. Raugi, Limit theorems for sequential expanding dynamical systems on [0,1],, in, 430 (2007), 89.
|
[10] |
W. Feller, "An Introduction to Probability Theory and its Applications,", Vol. II, (1971).
|
[11] |
V. F. Gaposhkin, Lacunary series and independent functions,, (Russian), 21 (1966), 3. Google Scholar |
[12] |
J. Komlós, A central limit theorem for multiplicative systems,, Canad. Math. Bull., 16 (1973), 67.
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.
|
[14] |
B. Petit, Le théorème limite central pour des sommes de Riesz-Raĭkov,, Probab. Theory Related Fields, 93 (1992), 407.
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.
doi: 10.1017/S0143385703000531. |
[16] |
A. Raugi, "Théorème Ergodique Multiplicatif, Produits de Matrices Aléatoires Indépendantes,", Publ. Inst. Rech. Math. Rennes, (1996). Google Scholar |
[17] |
M. Viana, "Stochastic Dynamics of Deterministic Systems,", Brazilian Math. Colloquium, (1997). Google Scholar |
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.
|
[2] |
A. Ayyer and M. Stenlund, Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms,, Chaos, 17 (2007).
|
[3] |
A. Ayyer, C. Liverani and M. Stenlund, Quenched CLT for random toral automorphism,, Discrete Contin. Dyn. Syst., 24 (2009), 331.
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.
|
[5] |
I. Berkes, On the asymptotic behaviour of $Sf(n_kx)$. Main theorems,, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 34 (1976), 319.
doi: 10.1007/BF00535967. |
[6] |
B. M. Brown, Martingale central limit theorems,, Annals of Math. Statistics, 42 (1971), 59.
|
[7] |
J.-P. Conze and S. Le Borgne, Limit law for some modified ergodic sums,, Stochastics and Dynamics, 11 (2011), 107.
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). Google Scholar |
[9] |
J.-P. Conze and A. Raugi, Limit theorems for sequential expanding dynamical systems on [0,1],, in, 430 (2007), 89.
|
[10] |
W. Feller, "An Introduction to Probability Theory and its Applications,", Vol. II, (1971).
|
[11] |
V. F. Gaposhkin, Lacunary series and independent functions,, (Russian), 21 (1966), 3. Google Scholar |
[12] |
J. Komlós, A central limit theorem for multiplicative systems,, Canad. Math. Bull., 16 (1973), 67.
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.
|
[14] |
B. Petit, Le théorème limite central pour des sommes de Riesz-Raĭkov,, Probab. Theory Related Fields, 93 (1992), 407.
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.
doi: 10.1017/S0143385703000531. |
[16] |
A. Raugi, "Théorème Ergodique Multiplicatif, Produits de Matrices Aléatoires Indépendantes,", Publ. Inst. Rech. Math. Rennes, (1996). Google Scholar |
[17] |
M. Viana, "Stochastic Dynamics of Deterministic Systems,", Brazilian Math. Colloquium, (1997). Google Scholar |
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