Proofs of the martingale FCLT

Details Proofs of the martingale FCLT Proofs of the martingale FCLT

2007-12-12

arxiv.org/abs/0712.1929v2

Probability Surveys 2007, Vol. 4, 268-302

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-PS122 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of

Scientific paper

10.1214/07-PS122

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.

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