Document Zbl 1003.60033

Exponential inequalities and functional central limit theorems for a random field. (English) Zbl 1003.60033

ESAIM, Probab. Stat. 5, 77-104 (2001).

The author presents new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, he gives sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform mixing random fields, the author requires both finite fourth moments and an algebraic decay of the mixing coefficients.

Reviewer: Zdzislaw Rychlik (Lublin)

Cited in 33 Documents

MSC:

60F17	Functional limit theorems; invariance principles
60G60	Random fields

Keywords:

functional central limit theorem; stationary random fields; exponential inequalities; mixing; metric entropy

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References:

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