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Large deviations for empirical measures of switching diffusion processes with small parameters

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Frontiers of Mathematics in China 2015年第4期10卷 949-963页

作者： Xiaocui MA Fubao XI School of Mathematics Beijing Institute of Technology Beijing 100081 China Department of Mathematics Jining University Qufu273155 China

We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small para... 详细信息

关键词： Switching diffusion process empirical measure large deviation

Unified Limits and Large Deviation Principles forβ-Laguerre Ensembles in Global Regime

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Acta Mathematica Sinica,English Series 2023年第7期39卷 1271-1288页

作者： Yu Tao MA School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of Education Beijing Normal UniversityBeijing 100875China

Let(λ_(1),...,λ_(n)) be β-Laguerre ensembles with parametersβ,p,n and μ_(n):=1/n∑^(n)_(i=1)δ_(Xi) with for 1≤i≤*** this paper,asβvaries and satisfies lim_(n→∞)log n/βn=0,we offer a modified Marchenko-Pastur,law or semicircle law as the weak limits for the sequence μ_(n) when lim_(n→∞)n/p=γ∈(0,1]or lim_(n→∞)n/p=0,*** recovers some well-known ***,we give a full large deviation principle of μ_(n) with speed βn^(2) and good rate function I_(γ) under the same condition to characterize the speed of the *** minimizer of I_(γ) is a modified Marchenko-Pastur law forγ∈(0,1]and the semicircle law forγ=0.

关键词： β-Laguerre ensemble large deviation principle empirical measure semicircular law Marchenko–Pastur law

RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS

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Acta Mathematica Scientia 2012年第5期32卷 1826-1834页

作者：高付清徐明周 School of Mathematics and Statistics Wuhan University

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.

关键词： sublinear expectation relative entropy large deviation empirical measure

LARGE DEVIATIONS FOR STATIONARY Φ-MIXING SEQUENCES IN τ-TOPOLOGY

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 149-158页

作者： Hu YIJUN Department of Mathematics, Wuhan University, Wuhan 430072, China. Department of Mathematics Wuhan University Wuhan 430072 China

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.

关键词： Large deviation empirical measure Stationary sequence Φ-mixing τ-topology

Upper Large Deviations for Mixing Random Sequence

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Communications in Mathematical Research 2010年第3期26卷 219-229页

作者： ZHANG YONG YANG XIAO-YUN DONG ZHI-SHAN Wang De-hui College of Mathematics Jilin University Changchun 130012

In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.

关键词： mixing sequence empirical measure large deviation