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Tanaka Formula and local time for a Class of Interacting Branching Measure-valued Diffusions

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1059-1098页

作者： Donald A.DAWSON Jean VAILLANCOURT Hao WANG School of Mathematics and Statistics Carleton UniversityOttawaCanada Department of Decision Sciences HECMontrealCanada Department of Mathematics University of OregonEugeneUSA

We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),... 详细信息

关键词： Measure-valued diffusions stochastic partial differential equations superprocesses branching processes local time Tanaka formula

Scaling limit of local time of Sinai＇s random walk

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Frontiers of Mathematics in China 2015年第6期10卷 1313-1324页

作者： Wenming HONG Hui YANG Ke ZHOU School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China School of Statistics University of International Business and Economics Beijing 100029China

We prove that the local times of a sequence of Sinai＇s random walks converge to those of Brox＇s diffusion by proper scaling. Our proof is based on the intrinsic branching structure of the random walk and the converg... 详细信息

关键词： Sinai's random walk random environment local time Brox's diffusion branching process

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

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Applied Mathematics and Mechanics(English Edition) 2009年第3期30卷 381-390页

作者：林正炎程宗毛 Xing-ming GUO Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China Institute of Applied Mathematics and Engineering Computation Hangzhou Dianzi University Hangzhou 310018 P. R. China 不详

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

关键词： multi-parameter fractional Lévy process fractional Brownian sheet local time Gaussian random field multi-parameter Poisson process multi-parameter Brownian motion

local time ANALYSIS OF ADDITIVE LVY PROCESSES WITH DIFFERENT LVY EXPONENTS

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Acta Mathematica Scientia 2009年第5期29卷 1155-1164页

作者：钟玉泉 School of Computer Panzhihua University

Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1）＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.

关键词： additive Levy processes local time HSlder laws

Generalized local time of the Indefinite Wiener Integral: White Noise Approach

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Journal of Mathematical Research with Applications 2012年第3期32卷 373-378页

作者： Jingjun GUO 1,2 1.School of Statistics,Lanzhou University of Finance and Economics,Gansu 730020,P.R.China 2.School of Mathematics and Statistics,Huazhong University of Science and Technology, Hubei 430074,P.R.China School of Statistics Lanzhou University of Finance and Economics School of Mathematics and Statistics Huazhong University of Science and Technology

In this paper,the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach,which means to regard the local time as a Hida distribution. Moreover,similar result is also obta... 详细信息

关键词： local time Hida distribution white noise approach.

local time of Additive Levy Process

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Wuhan University Journal of Natural Sciences 2000年第1期5卷 7-12页

作者： ZHONG Yu-quan HU Di-he ( College of Mathematics and Computer Science, Wuhan University, Wuhan 430072, China Department of Base, Panzhihua University, Sichuan 617000, China) Wuhan University College of Mathematics and Computer Science Wuhan China (GRID:grid.49470.3e) (ISNI:***) Panzhihua University Department of Base Sichuan China (GRID:grid.443521.5) Wuhan University College of Mathematics and Computer Science Wuhan China (GRID:grid.49470.3e) (ISNI:***)

We studied the problem of existence of jointly continuous local time for an additive process. Here, 'local time' is understood in the sence of occupation density, and by an additive Levy process we mean a process X = {X(t), t ∈ R^d_+ ) } which has the decomposition X= X_1, X_2 ... X_N. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can he obtained via Berman's method.

关键词： additive Levy process local time Levy process isotropic stable process

SOME LIMIT PROPERTIES OF local time FOR RANDOM WALK

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Applied Mathematics(A Journal of Chinese Universities) 2006年第1期21卷 87-95页

作者： Wen Jiwei Yan Yunliang Dept. of Math. Zhejiang Univ. Hangzhou 310028China Dept. of Management Zhejiang College of Traditional Chinese Medicine Hangzhou 310053China.

Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊（n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.

关键词： local time random walk precise asymptotic law of iterated logarithm strong approximation.

Smoothness of local times and self-intersection local times of Gaussian random fields

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Frontiers of Mathematics in China 2015年第4期10卷 777-805页

作者： Zhenlong CHEN DongshengWU Yimin XIAO School of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China Department of Mathematical Sciences University of Alabama in HuntsvilleHuntsville AL 35899 USA Department of Statistics and Probability Michigan State UniversityEast Lansing MI 48824 USA

This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.

关键词： Anisotropic Gaussian field local time collision local time,intersection local time self-intersection local time chaos expansion

Some Results on Fractional Brownian Sheets and Their local times

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 669-676页

作者： Zong-mao Chen Zheng-yan Lin Institute of Applied Mathematics and Engineering Computation Hangzhou Dianzi University Hangzhou310018 China Department of Mathematics Zhejiang University Hangzhou 310027 China

Let B0^H = {B0^H（t）,t ∈ R＋^N） be a real-valued fractional Brownian sheet. Define the （N,d）- Gaussian random field B^H by B^H（t） = （B1^H（t）,...,Bd^H（t）） t ∈ R＋^N, where B1^H, ..., Bd^H are independent copies of B0^H. The existence and joint continuity of local times of B^H is proven in some given conditions in [22]. We then study further properties of the local times of B^H, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].

关键词： Fractional Brownian sheet local time Hausdorff measure