Limit theorems for iterated random functions

DOI10.1239/jap/1082999076zbMath1046.60024OpenAlexW2146343663MaRDI QIDQ4819468

Publication date: 24 September 2004

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1082999076

zbMATH Keywords

cumulants exponential inequality Markov chain central limit theorem martingale stationarity nonlinear time series fractal Dini continuity iterated random function

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Functional limit theorems; invariance principles (60F17)

Related Items

A stochastic recurrence equations approach for score driven correlation models, A new bivariate integer-valued GARCH model allowing for negative cross-correlation, LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION FOR NONLINEAR PROCESSES, A LIMIT THEOREM FOR QUADRATIC FORMS AND ITS APPLICATIONS, A white noise test under weak conditions, Quantile spectral processes: asymptotic analysis and inference, Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables and winsorized mean, Inference for change points in high-dimensional data via selfnormalization, On maxima of periodograms of stationary processes, Local linear quantile estimation for nonstationary time series, Recursive estimation of time-average variance constants, TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS, Density estimation for nonlinear parametric models with conditional heteroscedasticity, A survey of average contractive iterated function systems, Self-normalized Cramér-type moderate deviations under dependence, Conditional value-at-risk: semiparametric estimation and inference, Statistical inference for nonparametric GARCH models, SEQUENTIAL TESTING FOR THE STABILITY OF HIGH-FREQUENCY PORTFOLIO BETAS, On convergence to stochastic integrals, A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation, Test of parameter changes in a class of observation-driven models for count time series, Local asymptotic powers of nonparametric and semiparametric tests for fractional integration, Convergence of covariance and spectral density estimates for high-dimensional locally stationary processes, An empirical central limit theorem for dependent sequences, ON SELF-NORMALIZATION FOR CENSORED DEPENDENT DATA, Sequential common change detection, isolation, and estimation in multiple poisson processes, Adaptive Change Point Monitoring for High-Dimensional Data, Kernel estimation for time series: an asymptotic theory, Asymptotic theory for curve-crossing analysis, Count Time Series: A Methodological Review, Spectral statistics of large dimensional Spearman's rank correlation matrix and its application, Berry-Esseen bounds for kernel estimates of stationary processes, Stationarity and ergodicity of univariate generalized autoregressive score processes, Rejoinder on: Some recent theory for autoregressive count time series, Adaptive Inference for Change Points in High-Dimensional Data, Time-varying multivariate causal processes, Edgeworth expansions for volatility models, Central limit theorems for high dimensional dependent data, Unnamed Item, Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices, Oscillations and moduli of continuity of kernel density estimators under dependence, Large deviation inequalities of Bayesian estimator in nonlinear regression models, Gaussian approximation for high dimensional vector under physical dependence, Empirical processes of iterated maps that contract on average, Covariance and precision matrix estimation for high-dimensional time series, Sequest: A Sequential Procedure for Estimating Quantiles in Steady-State Simulations, Uniform convergence rates for a class of martingales with application in non-linear cointegrating regression, Hypothesis testing for high-dimensional time series via self-normalization, Unnamed Item, A general approach to the joint asymptotic analysis of statistics from sub-samples, Komlós-Major-Tusnády approximation under dependence, Split invariance principles for stationary processes, Nonlinear system theory: Another look at dependence, Asymptotic spectral theory for nonlinear time series, Strong invariance principles for dependent random variables, A bootstrapped spectral test for adequacy in weak ARMA models, On the Komlós, Major and Tusnády strong approximation for some classes of random iterates, A note on the stability of multivariate non-linear time series with an application to time series of counts, Application of interval iterations to the entrainment problem in respiratory physiology, NONSTATIONARITY-EXTENDED WHITTLE ESTIMATION, Empirical processes of multidimensional systems with multiple mixing properties, Parametric and nonparametric models and methods in financial econometrics, On weak dependence conditions: the case of discrete valued processes, Flexible bivariate Poisson integer-valued GARCH model, An alternative to the coupling of Berkes-Liu-Wu for strong approximations, Asymptotic behavior for Markovian iterated function systems, \(M\)-estimation of linear models with dependent errors, Berry-Esseen theorems under weak dependence, Generalised kernel smoothing for non-negative stationary ergodic processes, Strong approximation for a class of stationary processes, Performance bounds for parameter estimates of high-dimensional linear models with correlated errors, New techniques for empirical processes of dependent data, An asymptotic theory for sample covariances of Bernoulli shifts, A bootstrap-assisted spectral test of white noise under unknown dependence, Postmodel selection estimators of variance function for nonlinear autoregression, On the recurrence set of planar Markov random walks, A unified stability theory for classical and monotone Markov chains, Asymptotic results for the empirical process of stationary sequences, Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes, Self-Excited Threshold Poisson Autoregression, Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series, Modeling and inference for multivariate time series of counts based on the INGARCH scheme, A FUNCTIONAL VERSION OF THE ARCH MODEL, A maximal 𝕃_{𝕡}-inequality for stationary sequences and its applications, Comments on: Some recent theory for autoregressive count time series, On the Bahadur representation of sample quantiles for dependent sequences, Time series analysis of COVID-19 infection curve: a change-point perspective, Asymptotic for LS estimators in the EV regression model for dependent errors, High dimensional generalized linear models for temporal dependent data, ITERATIONS OF DEPENDENT RANDOM MAPS AND EXOGENEITY IN NONLINEAR DYNAMICS, The integrated copula spectrum

Cites Work