The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Functional Central Limit Theorems

  • Werner Ploberger
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2591

Abstract

Functional limit theorems are generalizations of classical central limit theorems. They allow us not only to approximate the distributions of sums of random variables, but also describe their temporal evolution. The necessary mathematical concepts as well as some sufficient conditions for convergence to a random walk are discussed.

Keywords

Central limit theorems Convergence Functional limit theorems General limit theorems Gordin’s th Invariance principle Likelihood Lindeberg condition Martingale differences Random walk Separability Skorohod metric 

JEL Classifications

C10 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Andrews, D.W.K., and D. Pollard. 1994. An introduction to functional central limit theorems for dependent stochastic processes. Revue internationale de statistique 62: 119–132.Google Scholar
  2. Billingsley, P. 1999. Convergence of probability measures. 2nd ed. New York: Wiley-Interscience.CrossRefGoogle Scholar
  3. Davidson, J. 1994. Stochastic limit theory: An introduction for econometricians. Oxford: Oxford University Press.CrossRefGoogle Scholar
  4. McLeish, D.L. 1974. Dependent central limit theorems and invariance principles. Annals of Probability 2: 620–628.CrossRefGoogle Scholar
  5. Merlevede, F., M. Peligrad, and S. Utev. 2006. Recent advances in invariance principles for stationary sequences. Probability Surveys 3: 1–36.CrossRefGoogle Scholar
  6. Peligrad, M., and S. Utev. 2005. A new maximal inequality and invariance principle for stationary sequences. Annals of Probability 33: 789–815.CrossRefGoogle Scholar
  7. van der Vaart, A., and J.A. Wellner. 1996. Weak convergence and empirical processes. Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Werner Ploberger
    • 1
  1. 1.