Displaying similar documents to “A note on the Hájek-LeCam bound”

On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications

Silvia Vogel, Petr Lachout (2003)

Kybernetika

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Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.

On continuous convergence and epi-convergence of random functions. Part I: Theory and relations

Silvia Vogel, Petr Lachout (2003)

Kybernetika

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Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic...

Discrete limit theorems for general Dirichlet series. III

A. Laurinčikas, R. Macaitienė (2004)

Open Mathematics

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Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.