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 Probability Surveys > Vol. 4 (2007) open journal systems 

Proofs of the martingale FCLT

Ward Whitt, Columbia University

This is an expository review paper elaborating on the proof of the martingale functional central limit theorem (FCLT). This paper also reviews tightness and stochastic boundedness, highlighting one-dimensional criteria for tightness used in the proof of the martingale FCLT. This paper supplements the expository review paper Pang, Talreja and Whitt (2007) illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations.

AMS 2000 subject classifications: Primary 60F17, 60G44.

Keywords: functional central limit theorems, martingales, diffusion approximations, invariance principles.

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Whitt, Ward, Proofs of the martingale FCLT, Probability Surveys, 4, (2007), 268-302 (electronic). DOI: 10.1214/07-PS122.


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Probability Surveys. ISSN: 1549-5787