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Doukhan P. — Mixing. Properties and examples
Doukhan P. — Mixing. Properties and examples

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Название: Mixing. Properties and examples

Автор: Doukhan P.

Аннотация:

These notes are devoted to the study of mixing theory. The underlying goal is to provide statisticians dealing with problems involving weak dependence properties, with a powerful and easy tool. Up to now, this approach to dependence has been mainly considered from an abstract point of view. For an excellent review on this subject we refer to : "Dependence in Probability and Statistics, a Survey of Recent Results" (').
The aim of this work is to study applications of these results. We obtain bounds for the decay of mixing coefficient sequences associated to random processes or to random fields which are actually used in Statistics. In some cases we will give counterexamples which show that some frequently held ideas are wrong. In fact, it would be of little interest to study a probabilistic technique with no field of application.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 142

Добавлена в каталог: 04.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-mixing      3 17 32 45 57 80
$\alpha_{a,b}$-mixing      5 119
$\beta$-mixing      3 17 36 59 90
$\phi$-mixing      3 19 32 39 45 57 68 88 112
$\psi$-mixing      3 19 88
$\rho$-mixing      17 19 35 47 57 89
*-mixing      3 88
1-recurrent      105
Absolute regularity      3 7 90
Admissible      67
Affine models      97
Algebraic variety      96
annealing      95
Aperiodic      90 104
Aperiodic positive recurrent      89
AR(1) nonlinear process      104
arch      100
Arithmetic      106
ARMA      99
ARX nonlinear process      100
Bernstein inequality      33 36
Bilinear model      98
Birth-death      112
Brownian motion      112
c-mixing      16 18
C-set      89
Causal      79 85
Central limit theorem      45
Chapman — Kolmogorov      87
CLIQUE      69
Configuration      71
Covariance inequalities      10
Dependence      63
Derivation      116
Diffusion      116
Diffusion process      72 115
Dobrushin's condition      65
Doeblin recurrent      88
Dynamical system      93
Elliptic operator      115
Equilibrium      94
Ergodic      19 21 64 89 104 114
Feller      104
GARCH      100
Gaussian random field      57
Generator      116
Geometric ergodicity      89 104
Gibbs state      64
Hanis recurrent      90
Harmonic      61
Heteroscedastic      107
Hitting time      89
Hoeffding's inequality      33
Homogeneous      87
Hypercontractivity      119
Hypermixing      118
Infinitesimal operator      111
Interpolation lemma      27
Invariant      88
Invertibility condition      76
Irreducibility      104
k-Markovian      67
Kernel      63
Linear random field      75
Luxemburg norm      10
Lyapounov      94 102
m-dependent      17 57
m-irreducibility      90
Markov field      67 80
Markov process      87 112
Markov representation      98
Maximal inequalities      40
Measures of dependence      3
Mixing      21
Moving Average      81
Nearest neighbours      69
Nonhomogeneous      95
Null recurrent      22 89
Orlicz      10 46
Ornstein — Uhlenbeck      115 120
Ottaviani      42
Particle      71
Period      90
Petit set      89
Phase transition      64
Point process      71
Polynomial AR process      96
Positive recurrent      22 89
Potential      67
Probability kernel      63 87
Proper      63
Quasi-subadditive      40
r-mixing      15
Reconstruction      7
Recurrent      21 89
Regular      21 85
Renewal theory      106
Reversible      114
Riemanniann recurrence      89
Rosenthal inequality      27
Second order      84
Simulation      96
singular      85
Small set      89
Sobolev      122
Specification      64
Spectral density      58
Stable      94
Stationary      114
Stationary distribution      22 89
Strictly elliptic      122
Strong Feller      104
Strong mixing      3 26 75 120
Subadditive      42
Taboo      105
TAR(1)      104
Transition probability kernel      87
Ultracontractive      121
Uniform mixing      3 66
Uniformly ergodic      21
Unstable      94
Zariski      97
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