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The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations被引量：6
《Acta Mathematica Sinica,English Series》2020年第3期224-244,共21页Li Xin ZHANG 
Supported by grants from the NSF of China(Grant No.11731012);Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042);the 973 Program(Grant No.2015CB352302);the Fundamental Research Funds for the Central Universities。
Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distr...
关键词：Sub-linear EXPECTATION capacity INDEPENDENCE LEVY MAXIMAL inequality central limit theorem 
The Ergodicity of Stochastic Partial Differential Equations with Levy Jump
《Acta Mathematica Sinica,English Series》2011年第12期2415-2436,共22页Guo Li ZHOU Zhen Ting HOU 
Supported by the National Science Foundation of China （Grant Nos. 90820302, 11071258/A0110） and Fundamental Research Funds for the Central Universities （Grant No. CDJRC10100011）
In this article, the authors prove the uniqueness in law of a class of stochastic equations in infinite dimension, then we apply it to establish the existence and uniqueness of invariant measure of the generalized sto...
关键词：Stochastic partial differential equation Levy processes 
Stochastic Generalized Porous Media Equations with Levy Jump被引量：3
《Acta Mathematica Sinica,English Series》2011年第9期1671-1696,共26页Guo Li ZHOU Zhen TingHOU 
Supported by National Nature Science Foundation of China （Grant Nos. 10671212, 90820302） and Fundamental Research Funds for the Central Universities （Grant No. CDJRC10100011） The authors thanks Professor Dong Zhao for his valuable discussions and the authors would like to express their sincere gratitude to the referee for valuable comments and careful reading. They also appreciate that this paper has been improved greatly by the referee＇s advice.
In this paper, we first prove the existence and uniqueness of a general stochastic differential equation in finite dimension, then extend the result to the infinite dimension by the classical Galerkin method. As an ap...
关键词：Stochastic porous medium equation Levy processes 
On Exit Time from Balls of Jump-type Symmetric Markov Processes
《Acta Mathematica Sinica,English Series》2010年第1期185-192,共8页Toshihiro UEMURA 
Supported partly by Grand-in-Aid for Scientific Research (C)
We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the p...
关键词：symmetric Dirichlet form jump-type Markov process Levy system exit times from balls 
Stochastic Comparison and Preservation of Positive Correlations for Lévy-type Processes
《Acta Mathematica Sinica,English Series》2009年第5期741-758,共18页Jie Ming WANG 
Supported in part by Creative Research Group Fund of the National Natural Science Foundation of China (No. 10121101);the "985" Project from the Ministry of Education in China
The stochastic comparison and preservation of positive correlations for Levy-type processes on R^d are studied under the condition that Levy measure v satisfies f{0〈｜z｜≤1）｜z｜｜v（x, dz） - v（x, d（-z））｜ 〈 ...
关键词：stochastic comparison preservation of positive correlations Levy-type processes 
Explicit Forms of q-Deformed Lévy-Meixner Polynomials and Their Generating Functions
《Acta Mathematica Sinica,English Series》2008年第2期201-214,共14页Zhi Yuan HUANG Pei Yan LI Ying WU 
Project Nos.10571065 and 10401011 supported by NSFC
The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters： c1, c2,γ and β. In this paper, for-1 〈q〈 ...
关键词：Q-DEFORMATION Levy-Meixner polynomials generating function free probability 
A Nonstandard Lévy-Khintchine Formula and Lévy Processes
《Acta Mathematica Sinica,English Series》2008年第2期241-252,共12页Siu Ah NG 
Work completed at BiBoS Universitat Bielefeld in 2004 with support from Norway-SA Grant 2067063
We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary...
关键词：Levy processes Levy-Khintchine formula nonstandard analysis INFINITESIMAL hyperfinite 
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