Conditional principles for random weighted measures

Nathael Gozlan

ESAIM: Probability and Statistics (2005)

  • Volume: 9, page 283-306
  • ISSN: 1292-8100

Abstract

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In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form L n = 1 n ∑ i = 1 n Z i δ x i n , ( Z i ) i being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.

How to cite

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Gozlan, Nathael. "Conditional principles for random weighted measures." ESAIM: Probability and Statistics 9 (2005): 283-306. <http://eudml.org/doc/245918>.

@article{Gozlan2005,
abstract = {In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form $\{L_n=\frac\{1\}\{n\}\sum _\{i=1\}^nZ_i\delta _\{x_i^n\}\}$, $(Z_i)_i$ being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.},
author = {Gozlan, Nathael},
journal = {ESAIM: Probability and Statistics},
keywords = {large deviations; transportation cost inequalities; conditional laws of large numbers; minimum entropy methods; Large deviations},
language = {eng},
pages = {283-306},
publisher = {EDP-Sciences},
title = {Conditional principles for random weighted measures},
url = {http://eudml.org/doc/245918},
volume = {9},
year = {2005},
}

TY - JOUR
AU - Gozlan, Nathael
TI - Conditional principles for random weighted measures
JO - ESAIM: Probability and Statistics
PY - 2005
PB - EDP-Sciences
VL - 9
SP - 283
EP - 306
AB - In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form ${L_n=\frac{1}{n}\sum _{i=1}^nZ_i\delta _{x_i^n}}$, $(Z_i)_i$ being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.
LA - eng
KW - large deviations; transportation cost inequalities; conditional laws of large numbers; minimum entropy methods; Large deviations
UR - http://eudml.org/doc/245918
ER -

References

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