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Central limit theorem for random measures generated by stationary processes of compact sets

Zbyněk Pawlas (2003)

Kybernetika

Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.

Conditional principles for random weighted measures

Nathael Gozlan (2005)

ESAIM: Probability and Statistics

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.

Conditional principles for random weighted measures

Nathael Gozlan (2010)

ESAIM: Probability and Statistics

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 , ((Zi)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.

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