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central limit theorems FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

Acta Mathematica Scientia 2014年第2期34卷 501-512页

作者：高志强刘全升汪和松 Laboratory of Mathematics and Complex Systems School of Mathematical SciencesBeijing Normal University Univ. Bretagne-Sud CNRS UMR 6205LMBACampus de TohannicF-56000 VannesFrance School of Mathematics and Computing Science Changsha University of Science and Technology

We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.

关键词： Branching random walk random environment in time central limit theorems

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limit theorems for Inverse Process Tn of Hawkes Process

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Acta Mathematica Sinica,English Series 2017年第1期33卷 51-60页

作者： Youngsoo SEOL Department of Mathematics and Statistics University of South Florida Tampa FL 33620 USA

We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn

关键词： Hawkes processes self-exciting processes central limit theorems law of large numbers,large deviations

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Moderate deviation principle for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction

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Statistical Theory and Related Fields 2022年第4期6卷 299-308页

作者： Juan Yang School of Science Beijing University of Posts and TelecommunicationsBeijingPeople's Republic of China

In this article,we obtain a central limit theorem and prove a moderate deviation principle for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term.

关键词： Non-Lipschitz central limit theorems moderation deviations

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PARAMETER ESTIMATION FOR A DISCRETELY OBSERVED STOCHASTIC VOLATILITY MODEL WITH JUMPS IN THE VOLATILITY

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Chinese Annals of Mathematics,Series B 2003年第2期24卷 227-238页

作者： JIANGWENJIANG J.PEDERSEN SchoolofMathematicalScience YunnanNormalUniversityKunming650092China. InstituteofMathematicalSciences UniversityofAarhusAarhusDenmark.

In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.

关键词： Stochastic volatility models NIG distributions central limit theorems Law of large numbers Levy processes Ornstein-Uhlenbeck processes

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