Mixing Conditions, Central Limit Theorems and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences

2008 ◽  
Author(s):  
Nikolaos Kourogenis ◽  
Nikitas Pittis
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Mixing Conditions ◽  
Invariance Principles

Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes

1988 ◽  
Vol 4 (2) ◽  
pp. 210-230 ◽  
Author(s):  
Jeffrey M. Wooldridge ◽  
Halbert White
Keyword(s):  
Stochastic Processes ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Economic Time Series ◽  
Mixing Processes ◽  
Invariance Principles ◽  
Heterogeneous Processes ◽  
Economic Time ◽  
Unit Root Models

Building on work of McLeish, we present a number of invariance principles for doubly indexed arrays of stochastic processes which may exhibit considerable dependence, heterogeneity, and/or trending moments. In particular, we consider possibly time-varying functions of infinite histories of heterogeneous mixing processes and obtain general invariance results, with central limit theorems following as corollaries. These results are formulated so as to apply to economic time series, which may exhibit some or all of the features allowed in our theorems. Results are given for the case of both scalar and vector stochastic processes. Using an approach recently pioneered by Phillips, and Phillips and Durlauf, we apply our results to least squares estimation of unit root models.

scholarly journals A Note on the Central Limit Theorems for Dependent Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Distribution Functions ◽  
Central Limit Theorems ◽  
Cumulative Distribution ◽  
Characteristic Functions ◽  
Mixing Conditions ◽  
Cumulative Distribution Functions ◽  
Probability And Statistics

Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. By using characteristic functions, we obtain several limit theorems extending previous results.

scholarly journals Pressure Function and Limit Theorems for Almost Anosov Flows

2021 ◽  
Vol 382 (1) ◽  
pp. 1-47
Author(s):  
Henk Bruin ◽  
Dalia Terhesiu ◽  
Mike Todd
Keyword(s):  
Thermodynamic Properties ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stable Laws ◽  
Analytic Framework ◽  
Pressure Function ◽  
Hyperbolic Flows ◽  
Anosov Flows ◽  
Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

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