1974, Andhra University series, Volume no. 116, ix, 127, ii

Book

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2017, Volume 468, pp. 70 - 83

In recent years, China’s stock market has experienced dramatic fluctuations; in particular, in the second half of 2014 and 2015, the market rose sharply and...

Ergodic theorem | Linkage | Multi-dimensional stationary process | Testing program | Convergence | AUTOREGRESSIVE TIME-SERIES | PHYSICS, MULTIDISCIPLINARY | DICKEY-FULLER TEST | UNIT-ROOT | STATISTICAL ARBITRAGE | Stocks | Stock markets

Ergodic theorem | Linkage | Multi-dimensional stationary process | Testing program | Convergence | AUTOREGRESSIVE TIME-SERIES | PHYSICS, MULTIDISCIPLINARY | DICKEY-FULLER TEST | UNIT-ROOT | STATISTICAL ARBITRAGE | Stocks | Stock markets

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 01/2010, Volume 55, Issue 1, pp. 225 - 230

In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are...

Linear systems | Costs | random graph | Delay systems | Linear algebra | Consensus algorithm | Automatic control | Delay lines | ergodic stationary process | Polynomials | Modules (abstract algebra) | Arithmetic | Ergodic stationary process | Random graph | COORDINATION | RANDOM NETWORKS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Information networks | Ergodic theory | Usage | Analysis | Computer networks | Graph theory | Design and construction | Computer network protocols | Trees | Networks | Algorithms | Graphs | Random processes | Convergence | Ergodic processes

Linear systems | Costs | random graph | Delay systems | Linear algebra | Consensus algorithm | Automatic control | Delay lines | ergodic stationary process | Polynomials | Modules (abstract algebra) | Arithmetic | Ergodic stationary process | Random graph | COORDINATION | RANDOM NETWORKS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Information networks | Ergodic theory | Usage | Analysis | Computer networks | Graph theory | Design and construction | Computer network protocols | Trees | Networks | Algorithms | Graphs | Random processes | Convergence | Ergodic processes

Journal Article

2017, SpringerBriefs in Probability and Mathematical Statistics, ISBN 9783319623306

This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The...

Ergodic theory | Dynamics | Mathematics | Probabilities

Ergodic theory | Dynamics | Mathematics | Probabilities

Web Resource

The Annals of Probability, ISSN 0091-1798, 9/2010, Volume 38, Issue 5, pp. 2009 - 2022

We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT)...

Ergodic theory | Central limit theorem | Mathematical theorems | Stochastic processes | Stationary processes | Fourier transformations | Markov chains | Random variables | Martingales | Perceptron convergence procedure | Fourier transform | Stationary process | Spectral analysis | Martingale | PERIODOGRAM | central limit theorem | SERIES | stationary process | spectral analysis | martingale | STATISTICS & PROBABILITY | Mathematics - Probability | 60F17 | 60F05

Ergodic theory | Central limit theorem | Mathematical theorems | Stochastic processes | Stationary processes | Fourier transformations | Markov chains | Random variables | Martingales | Perceptron convergence procedure | Fourier transform | Stationary process | Spectral analysis | Martingale | PERIODOGRAM | central limit theorem | SERIES | stationary process | spectral analysis | martingale | STATISTICS & PROBABILITY | Mathematics - Probability | 60F17 | 60F05

Journal Article

Journal of the Royal Statistical Society. Series B (Statistical Methodology), ISSN 1369-7412, 3/2013, Volume 75, Issue 2, pp. 247 - 276

The inspection of residuals is a fundamental step for investigating the quality of adjustment of a parametric model to data. For spatial point processes, the...

Ergodic theory | Spatial points | Central limit theorem | Ergodic measures | Definiteness | Cubes | Mathematical vectors | Covariance matrices | Parametric models | Point estimators | Quadrat counting test | Campbell theorem | Central limit theorem for spatial random fields | Georgii Nguyen–Zessin formula | Maximum pseudolikelihood estimate | Georgii Nguyen-Zessin formula | PATTERNS | STATISTICS & PROBABILITY | ESTIMATOR | RANDOM-FIELDS | MODELS | POISSON PROCESSES | MAXIMUM PSEUDOLIKELIHOOD | Georgii NguyenZessin formula | CENTRAL-LIMIT-THEOREM | Studies | Statistical analysis | Equilibrium | Asymptotic methods | Errors | Null hypothesis | Asymptotic properties | Empirical equations | Consistency | Inspection | Inverse | Counting | Statistics | Statistics Theory | Mathematics

Ergodic theory | Spatial points | Central limit theorem | Ergodic measures | Definiteness | Cubes | Mathematical vectors | Covariance matrices | Parametric models | Point estimators | Quadrat counting test | Campbell theorem | Central limit theorem for spatial random fields | Georgii Nguyen–Zessin formula | Maximum pseudolikelihood estimate | Georgii Nguyen-Zessin formula | PATTERNS | STATISTICS & PROBABILITY | ESTIMATOR | RANDOM-FIELDS | MODELS | POISSON PROCESSES | MAXIMUM PSEUDOLIKELIHOOD | Georgii NguyenZessin formula | CENTRAL-LIMIT-THEOREM | Studies | Statistical analysis | Equilibrium | Asymptotic methods | Errors | Null hypothesis | Asymptotic properties | Empirical equations | Consistency | Inspection | Inverse | Counting | Statistics | Statistics Theory | Mathematics

Journal Article

7.
Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 05/2018, Volume 54, Issue 2, pp. 879 - 906

Journal Article

The Annals of Probability, ISSN 0091-1798, 5/2011, Volume 39, Issue 3, pp. 1137 - 1160

We study the problem of finding an universal estimation scheme h n : ℝ n → ℝ, n = 1, 2, ... which will satisfy $ \lim_{t\rightarrow \infty}...

Ergodic theory | Time series | Stationary processes | Time series forecasting | Mathematical inequalities | Mathematics | Martingales | Estimators | Perceptron convergence procedure | Ergodic processes | Nonparametric predicton | stationary processes | LARGE NUMBERS | LAW | OUTPUT | STATISTICS & PROBABILITY | ERGODIC TIME-SERIES | UNIVERSAL SCHEMES | Mathematics - Probability | 62G05 | 60G45 | 60G25

Ergodic theory | Time series | Stationary processes | Time series forecasting | Mathematical inequalities | Mathematics | Martingales | Estimators | Perceptron convergence procedure | Ergodic processes | Nonparametric predicton | stationary processes | LARGE NUMBERS | LAW | OUTPUT | STATISTICS & PROBABILITY | ERGODIC TIME-SERIES | UNIVERSAL SCHEMES | Mathematics - Probability | 62G05 | 60G45 | 60G25

Journal Article

Statistics, ISSN 0233-1888, 01/2014, Volume 48, Issue 1, pp. 121 - 128

Given a discrete-valued sample X 1 , ..., X n , we wish to decide whether it was generated by a distribution belonging to a family H 0 , or it was generated by...

stationary processes | composite hypotheses | ergodic processes | hypothesis testing | STATISTICS & PROBABILITY | Mathematics | Information Theory | Statistics | Statistics Theory | Computer Science

stationary processes | composite hypotheses | ergodic processes | hypothesis testing | STATISTICS & PROBABILITY | Mathematics | Information Theory | Statistics | Statistics Theory | Computer Science

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2014, Volume 50, Issue 1, pp. 256 - 284

We prove stable limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains...

One-sided law of iterated logarithm | Darling-Kac theorem | Stable limit | Transfer operator | Infinite invariant measure | Infinite ergodic theory | Mixing coefficient | Pointwise dual ergodic | MEASURE PRESERVING TRANSFORMATIONS | STATISTICS & PROBABILITY | RANDOM-VARIABLES | INVARIANT-MEASURES | LAWS | MAPS | PARTIAL-SUMS | 37A40 | 60Fxx | 60G10 | Darling–Kac theorem

One-sided law of iterated logarithm | Darling-Kac theorem | Stable limit | Transfer operator | Infinite invariant measure | Infinite ergodic theory | Mixing coefficient | Pointwise dual ergodic | MEASURE PRESERVING TRANSFORMATIONS | STATISTICS & PROBABILITY | RANDOM-VARIABLES | INVARIANT-MEASURES | LAWS | MAPS | PARTIAL-SUMS | 37A40 | 60Fxx | 60G10 | Darling–Kac theorem

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2005, Volume 133, Issue 1, pp. 285 - 293

We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are...

Ergodic theory | Central limit theorem | Mathematical theorems | Stationary processes | Time series | Fourier transformations | Markov chains | Mathematical functions | Random variables | Martingales | Linear process | Nonlinear time series | Fourier transformation | Periodogram | Spectral analysis | Martingale central limit theorem | MATHEMATICS | MATHEMATICS, APPLIED | periodogram | nonlinear time series | linear process | martingale central limit theorem

Ergodic theory | Central limit theorem | Mathematical theorems | Stationary processes | Time series | Fourier transformations | Markov chains | Mathematical functions | Random variables | Martingales | Linear process | Nonlinear time series | Fourier transformation | Periodogram | Spectral analysis | Martingale central limit theorem | MATHEMATICS | MATHEMATICS, APPLIED | periodogram | nonlinear time series | linear process | martingale central limit theorem

Journal Article

The Annals of Probability, ISSN 0091-1798, 1/2008, Volume 36, Issue 1, pp. 127 - 142

There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes..., X₋₁, X₀, X₁,... whose partial sums...

Ergodic theory | Central limit theorem | Mathematical theorems | Stationary processes | Partial sums | Logarithms | Martingales | Probabilities | Perceptron convergence procedure | Ergodic theorem | Markov chains | Operators on L | Fourier series | Conditional central limit question | MIXING SEQUENCES | ergodic theorem | martingales | STATISTICS & PROBABILITY | ADDITIVE-FUNCTIONALS | operators on L-2 | conditional central limit question | CENTRAL-LIMIT-THEOREM | RANDOM-VARIABLES | Mathematics - Probability | 60F05 | operators on L^2 | 60F15

Ergodic theory | Central limit theorem | Mathematical theorems | Stationary processes | Partial sums | Logarithms | Martingales | Probabilities | Perceptron convergence procedure | Ergodic theorem | Markov chains | Operators on L | Fourier series | Conditional central limit question | MIXING SEQUENCES | ergodic theorem | martingales | STATISTICS & PROBABILITY | ADDITIVE-FUNCTIONALS | operators on L-2 | conditional central limit question | CENTRAL-LIMIT-THEOREM | RANDOM-VARIABLES | Mathematics - Probability | 60F05 | operators on L^2 | 60F15

Journal Article

Machine Learning, ISSN 0885-6125, 06/2019, pp. 1 - 37

We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure...

Algorithms | Covariance | Clustering | Stochastic processes | Ergodic processes | Self-similarity

Algorithms | Covariance | Clustering | Stochastic processes | Ergodic processes | Self-similarity

Journal Article

08/2017, 1st ed. 2017, SpringerBriefs in Probability and Mathematical Statistics, ISBN 9783319623306, 143

This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The...

Gaussian processes | Dynamical Systems and Ergodic Theory | Probability Theory and Stochastic Processes | Mathematics

Gaussian processes | Dynamical Systems and Ergodic Theory | Probability Theory and Stochastic Processes | Mathematics

eBook

15.
Pointwise ergodic theorems with rate with applications to limit theorems for stationary processes

Stochastics and Dynamics, ISSN 0219-4937, 03/2011, Volume 11, Issue 1, pp. 135 - 155

We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving parallel to Sigma(n)(k=1) f o...

Ergodic theorems | quenched CLT | LIL | normal Markov chains | spectral theorem | MARTINGALE APPROXIMATIONS | MARKOV-CHAINS | STATISTICS & PROBABILITY | ADDITIVE-FUNCTIONALS

Ergodic theorems | quenched CLT | LIL | normal Markov chains | spectral theorem | MARTINGALE APPROXIMATIONS | MARKOV-CHAINS | STATISTICS & PROBABILITY | ADDITIVE-FUNCTIONALS

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 3/2012, Volume 25, Issue 1, pp. 171 - 188

In this paper we study the almost sure central limit theorem started at a point for additive functionals of a stationary and ergodic Markov chain via a...

Reversible Markov chains | Probability Theory and Stochastic Processes | Mathematics | 60J05 | Statistics, general | Quenched central limit theorem | 60F05 | 60F15 | ERGODIC-THEOREMS | STATISTICS & PROBABILITY | Markov processes

Reversible Markov chains | Probability Theory and Stochastic Processes | Mathematics | 60J05 | Statistics, general | Quenched central limit theorem | 60F05 | 60F15 | ERGODIC-THEOREMS | STATISTICS & PROBABILITY | Markov processes

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2009, Volume 256, Issue 6, pp. 1962 - 1997

We introduce a framework for the study of nonlinear homogenization problems in the setting of stationary continuous processes in compact spaces. The latter are...

Porous medium equation | Stationary ergodic processes | Algebras with mean value | Stochastic homogenization | Ergodic algebras | Two-scale Young measures | MATHEMATICS | 2-SCALE CONVERGENCE | EQUATIONS | CONSERVATION-LAWS | OPERATORS | Atmospheric radon

Porous medium equation | Stationary ergodic processes | Algebras with mean value | Stochastic homogenization | Ergodic algebras | Two-scale Young measures | MATHEMATICS | 2-SCALE CONVERGENCE | EQUATIONS | CONSERVATION-LAWS | OPERATORS | Atmospheric radon

Journal Article

The Annals of Probability, ISSN 0091-1798, 7/2004, Volume 32, Issue 3, pp. 2222 - 2260

We study stationary stable processes related to periodic and cyclic flows in the sense of Rosiński [Ann. Probab. 23 (1995) 1163-1187]. These processes are not...

Ergodic theory | Determinism | Lebesgue measures | Stationary processes | Lebesgue spaces | Fubinis theorem | Mathematical functions | Null set | Rotation | Borel sets | Cocycles | Flows | Stable stationary processes | Periodic and cyclic flows | MIXED MOVING AVERAGES | flows | cocycles | DECOMPOSITION | STATISTICS & PROBABILITY | periodic and cyclic flows | stable stationary processes | Mathematics - Probability | 37A40 | 60G10 | 60G52

Ergodic theory | Determinism | Lebesgue measures | Stationary processes | Lebesgue spaces | Fubinis theorem | Mathematical functions | Null set | Rotation | Borel sets | Cocycles | Flows | Stable stationary processes | Periodic and cyclic flows | MIXED MOVING AVERAGES | flows | cocycles | DECOMPOSITION | STATISTICS & PROBABILITY | periodic and cyclic flows | stable stationary processes | Mathematics - Probability | 37A40 | 60G10 | 60G52

Journal Article

The Annals of Probability, ISSN 0091-1798, 5/2012, Volume 40, Issue 3, pp. 1357 - 1374

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam...

Ergodic theory | Infinity | Mathematical transformations | Stationary processes | Coordinate systems | Mathematical vectors | Automorphisms | Dynamical systems | Probabilities | Stable stationary processes | Maharam system | Ergodic properties | STATISTICS & PROBABILITY | TRANSFORMATIONS | ergodic properties | Probability | Dynamical Systems | Mathematics | 37A50 | 37A40 | 60G10 | 60G52

Ergodic theory | Infinity | Mathematical transformations | Stationary processes | Coordinate systems | Mathematical vectors | Automorphisms | Dynamical systems | Probabilities | Stable stationary processes | Maharam system | Ergodic properties | STATISTICS & PROBABILITY | TRANSFORMATIONS | ergodic properties | Probability | Dynamical Systems | Mathematics | 37A50 | 37A40 | 60G10 | 60G52

Journal Article

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