Proofs of the martingale FCLT. (English) Zbl 1189.60070

Whitt, Ward

Probab. Surv. 4, 268-302 (2007).

Summary: 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 by G. Pang, R. Talreja andW. Whitt [Probab. Surv. 4, 193–267, electronic only (2007; Zbl 1189.60067)] illustrating the “martingale method” for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations.

MSC:

60F17	Functional limit theorems; invariance principles
60G44	Martingales with continuous parameter
60-02	Research exposition (monographs, survey articles) pertaining to probability theory

Keywords:

functional central limit theorems; martingales; diffusion approximations; invariance principles

Citations:

Zbl 1189.60067