Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker

ESAIM: Probability and Statistics (2010)

  • Volume: 5, page 77-104
  • ISSN: 1292-8100

Abstract

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We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give 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 ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients.

How to cite

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Dedecker, Jérôme. "Exponential inequalities and functional central limit theorems for random fields." ESAIM: Probability and Statistics 5 (2010): 77-104. <http://eudml.org/doc/197765>.

@article{Dedecker2010,
abstract = { We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give 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 ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. },
author = {Dedecker, Jérôme},
journal = {ESAIM: Probability and Statistics},
keywords = {Functional central limit theorem; stationary random fields; moment inequalities; exponential inequalities; mixing; metric entropy; chaining.; functional central limit theorem; exponential inequalities},
language = {eng},
month = {3},
pages = {77-104},
publisher = {EDP Sciences},
title = {Exponential inequalities and functional central limit theorems for random fields},
url = {http://eudml.org/doc/197765},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Dedecker, Jérôme
TI - Exponential inequalities and functional central limit theorems for random fields
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 77
EP - 104
AB - We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give 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 ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients.
LA - eng
KW - Functional central limit theorem; stationary random fields; moment inequalities; exponential inequalities; mixing; metric entropy; chaining.; functional central limit theorem; exponential inequalities
UR - http://eudml.org/doc/197765
ER -

References

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