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large deviation FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES

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Acta Mathematica Scientia 2007年第4期27卷 821-828页

作者：沈思 School of Mathematics and Statistics Wuhan University Wuhan 430072China Mathematics and Computer Sciences InstituteCentral University for NationaliticsBeijing 100081China

In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY （both known）, wherein the author gives two kinds of different proofs and gets the same results.

关键词： large deviation empirical correlation coefficient

large deviation for Supercritical Branching Processes with Immigration

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Acta Mathematica Sinica,English Series 2016年第8期32卷 893-900页

作者： Jing Ning LIU Mei ZHANG School of Mathematical Sciences Laboratory of Mathematics and Complex SystemsBeijing Normal University

In this paper, we study the large deviation for a supercritical branching process with immigration controlled by a sequence of non-negative integer-valued independently identical distributed random variables, improving the previous results for non immigration processes. We rely heavily on the detail description and limit property of the generating function of immigration processes.

关键词： Supercritical branching processes large deviation immigration

Rate Function of large deviation for a Class of Nonhomogeneous Markov Chains on Supercritical Percolation Network

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Acta Mathematica Sinica,English Series 2011年第9期27卷 1813-1830页

作者： Zhong Hao XU Dong HAN School of Finance and Statistics East China Normal University Shanghai 200241 P. R. China Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 P. R. China

We model an epidemic with a class of nonhomogeneous Markov chains on the supercritical percolation network on Zd. The large deviations law for the Markov chain is given. Explicit expression of the rate function for la... 详细信息

关键词： Nonhomogeneous Markov chain large deviation rate function percolation network

large and moderate deviation principles for susceptible-infected-removed epidemic in a random environment

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Frontiers of Mathematics in China 2021年第4期16卷 1117-1161页

作者： Xiaofeng XUE Yumeng SHEN School of Science Beijing Jiaotong UniversityBeijing 100044China

We are concerned with SIR epidemics in a random environment on complete graphs,where edges are assigned with i.i.d,weights.Our main results give large and moderate deviation principles of sample paths of this model.Our results generalize large and moderate deviation principles of the classic SIR models given by E.Pardoux and B.Samegni-Kepgnou[J.Appl.Probab.,2017,54:905-920]and X.F.Xue[Stochastic Process.Appl.,2019,140:49-80].

关键词： large deviation moderate deviation susceptible-infected-removed(SIR) epidemic random environment

A large deviation FOR OCCUPATIONTIMES OF SUPER-STABLE PROCESS

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Acta Mathematicae Applicatae Sinica 1999年第3期15卷 240-248页

作者：张连增 Department of Risk Management and Insurance Nankai University Tianjing China

I. Iscoe and T.Y. Lee started the study of large deviation for measure-valued Markovprocesses in the case of super-Brownian motion. We generalized their results to the case ofsuper-stable case. The self-similarity pro... 详细信息

关键词： large deviation super-stable process self-similarity

large deviation on Random Sums for a Double Type-insurance Risk Model

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Large Deviation on Random Sums for a Double Type-insurance R...

large deviationS FOR TOP EIGENVALUES OFβ-JACOBI ENSEMBLES AT SCALING TEMPERATURES

2009 International Conference on Computational Intelligence and Natural Computing(CINC 2009)

作者： ZHAN Xiao-lin School of Science Shanghai Second Polytechnic University Shanghai China YU Li School of Science Hefei University of Technology Hefei China

A double-type-insurance risk model with heavy tails was defined and studied in ref. [1]. A further investigation into the large deviation on random sums under the distribution of dominated variation （D class） is pre... 详细信息

关键词： double type-insurance risk model heavy tails random sums large deviation dominated variation

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Acta Mathematica Scientia 2023年第4期43卷 1767-1780页

作者：雷良贞马宇韬 School of Mathematical Science Capital Normal UniversityBeijing 100048China School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of Education Beijing Normal UniversityBeijing 100875China

Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγ0 via the large deviation of the corresponding empirical measure and via a direct e... 详细信息

Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγlarge deviation for p_(1)+p_(2)/p_(1)■λ_(i)whenγ>0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,whenγ=0.

关键词： β-Jacobi ensemble large deviation Wachter law extremal eigenvalue

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

large deviationS AND MODERATE deviationS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

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Acta Mathematica Scientia 2011年第1期31卷 344-352页

作者：刘莉万成高冯艳钦 School of Mathematics and Statistics Wuhan University School of Mathmatics and Computer Science Hubei University

In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.

关键词： large deviation moderate deviation negative dependence non-identical distribution