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Stochastic Limit Theory has become a standard reference in its field. This new edition offers updated and improved results and an extended range of topics. It works both as a textbook and as an account of recent work in a field of particular interest to econometricians.

Econometrics --- Limit theorems (Probability theory) --- Econometrics. --- Stochastic processes. --- Random processes --- Probabilities --- Economics, Mathematical --- Statistics

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The analysis and modeling of time series is of the utmost importance in various fields of application. This Special Issue is a collection of articles on a wide range of topics, covering stochastic models for time series as well as methods for their analysis, univariate and multivariate time series, real-valued and discrete-valued time series, applications of time series methods to forecasting and statistical process control, and software implementations of methods and models for time series. The proposed approaches and concepts are thoroughly discussed and illustrated with several real-world data examples.

Humanities --- time series --- anomaly detection --- unsupervised learning --- kernel density estimation --- missing data --- multivariate time series --- nonstationary --- spectral matrix --- local field potential --- electric power --- forecasting accuracy --- machine learning --- extended binomial distribution --- INAR --- thinning operator --- time series of counts --- unemployment rate --- SARIMA --- SETAR --- Holt–Winters --- ETS --- neural network autoregression --- Romania --- integer-valued time series --- bivariate Poisson INGARCH model --- outliers --- robust estimation --- minimum density power divergence estimator --- CUSUM control chart --- INAR-type time series --- statistical process monitoring --- random survival rate --- zero-inflation --- cointegration --- subspace algorithms --- VARMA models --- seasonality --- finance --- volatility fluctuation --- Student’s t-process --- entropy based particle filter --- relative entropy --- count data --- time series analysis --- Julia programming language --- ordinal patterns --- long-range dependence --- multivariate data analysis --- limit theorems --- integer-valued moving average model --- counting series --- dispersion test --- Bell distribution --- count time series --- estimation --- overdispersion --- multivariate count data --- INGACRCH --- state-space model --- bank failures --- transactions --- periodic autoregression --- integer-valued threshold models --- parameter estimation --- models

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The analysis and modeling of time series is of the utmost importance in various fields of application. This Special Issue is a collection of articles on a wide range of topics, covering stochastic models for time series as well as methods for their analysis, univariate and multivariate time series, real-valued and discrete-valued time series, applications of time series methods to forecasting and statistical process control, and software implementations of methods and models for time series. The proposed approaches and concepts are thoroughly discussed and illustrated with several real-world data examples.

Humanities --- time series --- anomaly detection --- unsupervised learning --- kernel density estimation --- missing data --- multivariate time series --- nonstationary --- spectral matrix --- local field potential --- electric power --- forecasting accuracy --- machine learning --- extended binomial distribution --- INAR --- thinning operator --- time series of counts --- unemployment rate --- SARIMA --- SETAR --- Holt–Winters --- ETS --- neural network autoregression --- Romania --- integer-valued time series --- bivariate Poisson INGARCH model --- outliers --- robust estimation --- minimum density power divergence estimator --- CUSUM control chart --- INAR-type time series --- statistical process monitoring --- random survival rate --- zero-inflation --- cointegration --- subspace algorithms --- VARMA models --- seasonality --- finance --- volatility fluctuation --- Student’s t-process --- entropy based particle filter --- relative entropy --- count data --- time series analysis --- Julia programming language --- ordinal patterns --- long-range dependence --- multivariate data analysis --- limit theorems --- integer-valued moving average model --- counting series --- dispersion test --- Bell distribution --- count time series --- estimation --- overdispersion --- multivariate count data --- INGACRCH --- state-space model --- bank failures --- transactions --- periodic autoregression --- integer-valued threshold models --- parameter estimation --- models

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The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.

Research & information: general --- Mathematics & science --- continuous-time Markov chains --- non-stationary Markovian queueing model --- stability --- perturbation bounds --- forward Kolmogorov system --- threshold processing --- random samples --- long-term dependence --- mean-square risk estimate --- integrals and sums --- rates of convergence --- conditional law of large numbers --- conditional central limit theorem --- stochastic differential observation system --- nonlinear filtering problem --- state-dependent observation noise --- numerical filtering algorithm --- filtering given time-discretized observations --- stable approximation --- approximation accuracy --- Rényi theorem --- Kantorovich distance --- zeta-metrics --- Stein’s method --- stationary renewal distribution --- equilibrium transform --- geometric random sum --- characteristic function --- precipitation --- limit theorems --- statistical test --- generalized negative binomial distribution --- generalized gamma distribution --- asymptotic approximations --- extreme order statistics --- random sample size --- slowly varying --- monotony in the Zygmund sense --- class Γa(g) --- self-neglecting function --- convergence rates --- citation distribution --- Hirsch index --- geometric distribution --- Sibuya distribution --- geometrically stable distribution --- generalized Linnik distribution --- random sum --- transfer theorem --- multivariate normal scale mixtures --- heavy-tailed distributions --- multivariate stable distribution --- multivariate Linnik distribution --- generalized Mittag–Leffler distribution --- multivariate generalized Mittag–Leffler distribution --- stable distribution --- probability density function --- distribution function --- Hankel contours --- multivariate stable processes --- contour integrals --- fractional laplacian --- second order expansions --- high-dimensional --- low sample size --- Laplace distribution --- Student’s t-distribution --- pareto mixture distribution --- multiserver system --- uniform distance --- perfect simulation --- priority system --- marked Markov arrival process --- phase-type distribution --- change of the priority --- dispatching --- heterogeneous servers --- Markov decision process --- policy-iteration algorithm --- mean number of customers --- decomposable semi-regenerative process --- multiple power series distribution --- integral limit theorem --- local limit theorem --- Tauberian lemma --- R-weakly one-sided oscillation of the multiple sequence at infinity along the given multiple sequence --- pension schemes --- balance equation --- gross premium --- premium load --- lump sum --- defined contribution pension schemes --- decrement tables --- robustness --- minimax approach --- stable estimation