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Multifractal structure of the product measure of two independent general subordinators'occupation measures

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Science China Mathematics 2009年第8期52卷 1785-1795页

作者： KONG LingTao HU XiaoYu School of Mathematics Graduate University of the Chinese Academy of SciencesBeijing 100049China

In this paper, we mainly investigate the multifractal spectrum of the random measure derived from two independent general subordinators.

关键词： general subordinator occupation measure Hausdor measure multifractal spetrum

occupation measures of Singularly Perturbed Markov Chains with Absorbing States

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Acta Mathematica Sinica,English Series 2000年第1期16卷 161-180页

作者： G.Yin~(1)) Department of Mathematics,Wayne State University,Detroit,MI 48202,USAQ.Zhang~(2)) Department of Mathematics,University of Georgia,Athens,GA 30602,USAG.Badowski~(3)) Department of Mathematics,Wayne State University,Detroit,MI 48202,USA Department of Mathematics Wayne State University Detroit MI 48202 USA Department of Mathematics University of Georgia Athens GA 30602 USA

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimate is obtained.By averaging the fast components,we obtain an aggregated process.Although the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state space.Moreover,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

关键词： Singularly perturbed Markov chain occupation measure Aggregation Absorbing state Weak convergence Switching diffusion

Large deviation principle of occupation measures for non-linear monotone SPDEs

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Science China Mathematics 2021年第4期64卷 799-822页

作者： Ran Wang Jie Xiong Lihu Xu School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Department of Mathematics Faculty of Science and TechnologyUniversity of MacaoMacaoChina

Using the hyper-exponential recurrence criterion,we establish the occupation measures’large deviation principle for a class of non-linear monotone stochastic partial differential equations(SPDEs)driven by Wiener noise,including the stochastic p-Laplace equation,the stochastic porous medium equation and the stochastic fast-diffusion equation.We also propose a framework for verifying hyper-exponential recurrence,and apply it to study the large deviation problems for strong dissipative SPDEs.These SPDEs can be stochastic systems driven by heavy-tailedα-stable process.

关键词： stochastic partial differential equation large deviation principle occupation measure hyperexponential recurrence