Convergence of Distributions Generated by Stationary Stochastic Processes

Previous article Next article Convergence of Distributions Generated by Stationary Stochastic ProcessesYu. A. DavydovYu. A. Davydovhttps://doi.org/10.1137/1113086PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. A. Volkonskii˘ and , Yu. A. Rozanov, Some limit theorems for random functions. I, Theor. Probability Appl., 4 (1959), 178–197 MR0121856 0092.33502 LinkGoogle Scholar[2] I. I. Gikhman and , A. V. Skorokhod, Introduction to the Theory of Stochastic Processes, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[3] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[4] I. A. Ibragimov and , Yu. V. Linnik, Independent and Stationarily Related Random Variables, Iz-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[5] Yu. V. Prokhorov, Convergence of stochastic processes and limit theorems in probability theory, Theory Prob. Applications, 1 (1956), 157–214 10.1137/1101016 LinkGoogle Scholar[6] R. Z. Khas'minskii, On stochastic processes defined by differential equations with a small parameter, Theory Prob. Applications, 11 (1966), 211–228 10.1137/1111018 0168.16002 LinkGoogle Scholar[7] R. Z. Khas'minskii, A limit theorem for the solutions of differential equations with random right-hand sides, Theory Prob. Applications, 11 (1966), 390–406 10.1137/1111038 LinkGoogle Scholar[8] Patrick Billingsley, The invariance principle for dependent random variables, Trans. Amer. Math. Soc., 83 (1956), 250–268 MR0090923 0075.13703 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Optimal covariance matrix estimation for high-dimensional noise in high-frequency dataJournal of Econometrics, Vol. 109 | 1 Sep 2022 Cross Ref Partial functional linear regression with autoregressive errorsCommunications in Statistics - Theory and Methods, Vol. 51, No. 13 | 28 September 2020 Cross Ref Goodness-of-Fit Tests for SPARMA Models with Dependent Error TermsJournal of Time Series Econometrics, Vol. 14, No. 2 | 3 February 2022 Cross Ref Peaks, gaps, and time‐reversibility of economic time seriesJournal of Time Series Analysis, Vol. 86 | 25 May 2022 Cross Ref Asymptotic theory for the inference of the latent trawl model for extreme valuesScandinavian Journal of Statistics | 2 February 2022 Cross Ref Averaging Principles for Stochastic 2D Navier–Stokes EquationsJournal of Statistical Physics, Vol. 186, No. 2 | 16 January 2022 Cross Ref Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errorsComputational Statistics & Data Analysis, Vol. 165 | 1 Jan 2022 Cross Ref A more powerful test of equality of high-dimensional two-sample meansComputational Statistics & Data Analysis, Vol. 164 | 1 Dec 2021 Cross Ref Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity modelJournal of Econometrics, Vol. 224, No. 2 | 1 Oct 2021 Cross Ref Edge-Preserving Denoising of Image SequencesEntropy, Vol. 23, No. 10 | 12 October 2021 Cross Ref Kernel-based prediction of non-Markovian time seriesPhysica D: Nonlinear Phenomena, Vol. 418 | 1 Apr 2021 Cross Ref Averaging Principle for Complex Ginzburg--Landau Equation Perturbated by Mixing Random ForcesPeng GaoSIAM Journal on Mathematical Analysis, Vol. 53, No. 1 | 4 January 2021AbstractPDF (588 KB)Nonparametric estimation of infinite order regression and its application to the risk-return tradeoffJournal of Econometrics, Vol. 219, No. 2 | 1 Dec 2020 Cross Ref Maximum and Shape of Interfaces in 3D Ising CrystalsCommunications on Pure and Applied Mathematics, Vol. 44 | 1 November 2020 Cross Ref Copula estimation through waveletsBrazilian Journal of Probability and Statistics, Vol. 34, No. 3 | 1 Aug 2020 Cross Ref The asymptotic distribution of CUSUM estimator based on α -mixing sequencesCommunications in Statistics - Simulation and Computation, Vol. 29 | 20 July 2020 Cross Ref Estimation of weak ARMA models with regime changesStatistical Inference for Stochastic Processes, Vol. 23, No. 1 | 12 July 2019 Cross Ref Asymptotic Theory for the Inference of the Latent Trawl Model for Extreme ValuesSSRN Electronic Journal, Vol. 115 | 1 Jan 2020 Cross Ref Panel data analysis with heterogeneous dynamicsJournal of Econometrics, Vol. 212, No. 2 | 1 Oct 2019 Cross Ref A central limit theorem for functions of stationary max-stable random fields on RdStochastic Processes and their Applications, Vol. 129, No. 9 | 1 Sep 2019 Cross Ref The unusual properties of aggregated superpositions of Ornstein–Uhlenbeck type processesBernoulli, Vol. 25, No. 3 | 1 Aug 2019 Cross Ref Spatial Risk Measures and Rate of Spatial DiversificationRisks, Vol. 7, No. 2 | 2 May 2019 Cross Ref Distribution of residual autocorrelations for multiplicative seasonal ARMA models with uncorrelated but nonindependent error termsStatistica Neerlandica, Vol. 59 | 3 May 2019 Cross Ref ReferencesGARCH Models | 25 March 2019 Cross Ref Non-parametric regression for spatially dependent data with waveletsStatistics, Vol. 52, No. 6 | 7 August 2018 Cross Ref A Bernstein inequality for exponentially growing graphsCommunications in Statistics - Theory and Methods, Vol. 47, No. 20 | 20 November 2017 Cross Ref On the History of the St. Petersburg School of Probability and Statistics. 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Theory and Methods, Vol. 30, No. 2 | 28 Mar 2001 Cross Ref Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under α-Mixing DependenceJournal of Multivariate Analysis, Vol. 73, No. 1 | 1 Apr 2000 Cross Ref Covariance matrix estimation for estimators of mixing weak ARMA modelsJournal of Statistical Planning and Inference, Vol. 83, No. 2 | 1 Feb 2000 Cross Ref Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal DistributionLimit Theorems of Probability Theory | 1 Jan 2000 Cross Ref Estimation du comportement asymptotique des autocovariances et autocorrélations empiriques de processus multivariéeasCanadian Journal of Statistics, Vol. 27, No. 3 | 1 Sep 1999 Cross Ref Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resettingIEEE Transactions on Automatic Control, Vol. 44, No. 5 | 1 May 1999 Cross Ref On the subsample bootstrap variance estimationTest, Vol. 7, No. 2 | 1 Dec 1998 Cross Ref Last passage time for the empirical mean of some mixing processesStatistics & Probability Letters, Vol. 40, No. 3 | 1 Oct 1998 Cross Ref Contracting in space: An application of spatial statistics to discrete-choice modelsJournal of Econometrics, Vol. 85, No. 1 | 1 Jul 1998 Cross Ref Estimating linear representations of nonlinear processesJournal of Statistical Planning and Inference, Vol. 68, No. 1 | 1 May 1998 Cross Ref Estimation de la précision asymptotique dans l'estimation de modèles ARMA faiblesComptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 326, No. 3 | 1 Feb 1998 Cross Ref On the Kolmogorov--Hajek--Rényi Inequality for Normed Integrals of Weakly Dependent ProcessesTheory of Probability & Its Applications, Vol. 42, No. 2 | 17 February 2012AbstractPDF (271 KB)The Bootstrap of Empirical Processes for α-Mixing SequencesHigh Dimensional Probability | 1 Jan 1998 Cross Ref Random central limit theorem for the linear process generated by a strong mixing processStatistics & Probability Letters, Vol. 35, No. 2 | 1 Sep 1997 Cross Ref Nonparametric inference for thinned point processStatistics & Probability Letters, Vol. 33, No. 3 | 1 May 1997 Cross Ref The bootstrap for empirical processes based on stationary observationsStochastic Processes and their Applications, Vol. 65, No. 2 | 1 Dec 1996 Cross Ref The bootstrap of the mean for strong mixing sequences under minimal conditionsStatistics & Probability Letters, Vol. 28, No. 1 | 1 Jun 1996 Cross Ref Limit Theorems for the Scheme of Series for Weakly Dependent VariablesTheory of Probability & Its Applications, Vol. 40, No. 4 | 12 July 2006AbstractPDF (922 KB)A Functional Limit Theorem for Random Variables with Strong Residual DependenceTheory of Probability & Its Applications, Vol. 40, No. 4 | 12 July 2006AbstractPDF (1917 KB)Inequalities for mixing processesNonparametric Statistics for Stochastic Processes | 1 Jan 1996 Cross Ref A note on moment bounds for strong mixing sequencesStatistics & Probability Letters, Vol. 16, No. 2 | 1 Jan 1993 Cross Ref ADAPTIVE SEMIPARAMETRIC ESTIMATION IN THE PRESENCE OF AUTOCORRELATION OF UNKNOWN FORMJournal of Time Series Analysis, Vol. 13, No. 1 | 1 Jan 1992 Cross Ref Nonparametric regression estimation in models with weak error's structureJournal of Multivariate Analysis, Vol. 37, No. 2 | 1 May 1991 Cross Ref The Central Limit Theorem for Empirical Moment Generating FunctionsTheory of Probability & Its Applications, Vol. 34, No. 2 | 17 July 2006AbstractPDF (386 KB)Cumulants and Moment InequalitiesTheory of Probability & Its Applications, Vol. 34, No. 4 | 17 July 2006AbstractPDF (515 KB)On the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equationsApplied Mathematics & Optimization, Vol. 20, No. 1 | 1 Jul 1989 Cross Ref On a class of mixing processesStochastics and Stochastic Reports, Vol. 26, No. 3 | 2 May 2007 Cross Ref Averaging and fluctuations for parabolic equations with rapidly oscillating random coefficientsProbability Theory and Related Fields, Vol. 77, No. 3 | 1 Mar 1988 Cross Ref The central limit theorem for summability methods of some weakly dependent sequencesStatistics & Probability Letters, Vol. 5, No. 2 | 1 Mar 1987 Cross Ref Moment inequalities for mixing sequences of random variablesStochastic Analysis and Applications, Vol. 5, No. 1 | 1 Jan 1987 Cross Ref Invariance principles under a two-part mixing assumptionStochastic Processes and their Applications, Vol. 22, No. 2 | 1 Jul 1986 Cross Ref Recent Advances in the Central Limit Theorem and Its Weak Invariance Principle for Mixing Sequences of Random Variables (A Survey)Dependence in Probability and Statistics | 1 Jan 1986 Cross Ref Gradient procedures for stochastic approximation with dependent noise and their asymptotic behaviourInternational Journal of Systems Science, Vol. 16, No. 8 | 10 May 2007 Cross Ref Multilinear forms and measures of dependence between random variablesJournal of Multivariate Analysis, Vol. 16, No. 3 | 1 Jun 1985 Cross Ref A functional central limit theorem for strongly mixing sequences of random variablesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 69, No. 4 | 1 Jan 1985 Cross Ref The rate of convergence of the least squares estimator in a non-linear regression model with dependent errorsJournal of Multivariate Analysis, Vol. 14, No. 3 | 1 Jun 1984 Cross Ref On the Convergence Rate in the Invariance Principle for Strongly Mixing SequencesTheory of Probability & Its Applications, Vol. 28, No. 4 | 28 July 2006AbstractPDF (532 KB)The Central Limit Theorem for Weakly Dependent Banach-Valued VariablesTheory of Probability & Its Applications, Vol. 28, No. 1 | 17 July 2006AbstractPDF (1120 KB)Diffusion approximations of some stochastic difference equations. IIHiroshima Mathematical Journal, Vol. 14, No. 1 | 1 Jan 1984 Cross Ref NONPARAMETRIC ESTIMATORS FOR TIME SERIESJournal of Time Series Analysis, Vol. 4, No. 3 | 1 May 1983 Cross Ref The invariance principle for ϕ-mixing sequencesZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 63, No. 1 | 1 Mar 1983 Cross Ref The Invariance Principle for Stationary Random Fields with a Strong Mixing ConditionTheory of Probability & Its Applications, Vol. 27, No. 2 | 17 July 2006AbstractPDF (437 KB)A note on the weak convergence of solutions of certain stochastic ordinary differential equationsProbability Theory and Mathematical Statistics | 11 September 2006 Cross Ref Invariance principle for estimates of regression coefficients of a random fieldUkrainian Mathematical Journal, Vol. 33, No. 6 | 1 Jan 1982 Cross Ref On the Convergence Rate in the Central Limit Theorem for Weakly Dependent Random VariablesTheory of Probability & Its Applications, Vol. 25, No. 4 | 17 July 2006AbstractPDF (1254 KB)On the chernoff-savage theorem for dependent sequencesAnnals of the Institute of Statistical Mathematics, Vol. 32, No. 1 | 1 Dec 1980 Cross Ref Empirical distribution functions and functions of order statistics for mixing random variablesJournal of Multivariate Analysis, Vol. 10, No. 3 | 1 Sep 1980 Cross Ref Summary of Papers Presented at Sessions of the Probability and Statistics Seminar at The T. G. Shevchenko Kiev State University, 1978Theory of Probability & Its Applications, Vol. 24, No. 3 | 17 July 2006AbstractPDF (569 KB) 1980 Cross Ref Moment bounds for stationary mixing sequencesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 52, No. 1 | 1 Jan 1980 Cross Ref On the Invariance Principle for Homogeneous and Isotropic Random of Probability & Its Applications, Vol. 24, No. 1 | 17 July 2006AbstractPDF rates of the strong for stationary mixing sequencesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 49, No. 1 | 1 Jan Cross Ref The for strong mixing sequences of and their applications to Mathematical Journal, Vol. No. 2 | 1 Jan Cross Ref Limit Measures in the Asymptotic Theory of of Probability & Its Applications, Vol. 23, No. 1 | 17 July 2006AbstractPDF inequalities for mixing Mathematical Journal, Vol. No. 2 | 1 Jan Cross Ref A on Random of Probability & Its Applications, Vol. 21, No. 4 | 17 July 2006AbstractPDF KB)A on the Central Limit Theorems for Dependent Random VariablesTheory of Probability & Its Applications, Vol. 20, No. 1 | 17 July 2006AbstractPDF principles for dependent variablesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 32, No. 3 | 1 Jan Cross Ref Weak convergence of empirical processes for strong mixing sequences of stochastic f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 33, No. 2 | 1 Jan Cross Ref On the central limit theorem for stationary f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 30, No. 4 | 1 Jan Cross Ref Functional central limit theorems for stationary processes the strong mixing Mathematical Journal, Vol. 24, No. 3 | 1 Jan Cross Ref The Invariance Principle for Stationary ProcessesTheory of Probability & Its Applications, Vol. No. 3 | 17 July 2006AbstractPDF to the of the of the to in in | 1 Jan Cross Ref on some of the on Probability Theory and Statistics Cross Ref 13, of Probability & Its History January July 2006 for and Applied & for and Applied Mathematics