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Fixed points of smoothing transformation in random environment

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Frontiers of Mathematics in China 2021年第4期16卷 1191-1210页

作者： Xiaoyue ZHANG wenming hong School of Statistics Capital University of Economics and BusinessBeijing 100070China School of Mathematical Sciences Laboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijing 100875China

At each time n∈N,let Y^(n)(ξ)=(y^(n)_(1)(ξ),y^(n)_(2)(ξ),…)be a random sequence of non-negative numbers that are ultimately zero in a random environmentξ=(ξ_(n))n∈*** existence and uniqueness of the non-negative fixed points of the associated smoothing transformation in random environment are *** fixed points are solutions to the distributional equation for a.e.ξ,Z(ξ)=dΣ_(i∈N_(+))y^(0)_(i)(ξ)Z^(1)_(i)(ξ),where{Z^(1)_(i):i∈N_(+)}are random variables in random environment which satisfy that for any environmentξ,under P_(ξ),{Z^(1)_(i)(ξ):i∈N_(+)}are independent of each other and Y^(0)(ξ),and have the same conditional distribution P_(ξ)(Z^(1)_(i)(ξ)∈·)=P_(Tξ)(Z(Tξ)∈·),where T is the shift *** extends the classical results of ***[***.,1977,14:25-37]to the random environment *** an application,the martingale convergence of the branching random walk in random environment is given as well.

关键词： Smoothing transformation functional equation branching random walk random environment martingales

On the transience and recurrence of Lamperti’s random walk on Galton-Watson trees

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Science China Mathematics 2019年第9期62卷 1813-1822页

作者： wenming hong Minzhi Liu School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University

In a Galton-Watson tree generated by a supercritical branching process with offspring N and EN =:m > 1, the conductance assigned to the edge between the vertex x and its parent x* is denoted by C(x) and given by C(x) =(λ +A/|x|α)-|x|, where |x| is the generation of the vertex x. For(Xn)n≥0, a C(x)-biased random walk on the tree, we show that (1) when λ≠ m, α > 0,(Xn)n≥0 is transient/recurrent according to whether λ m, respectively;(2) when λ = m, 0 0, *** particular, if P(N = 1) = 1, the C(x)-biased random walk is Lamperti’s random walk on the nonnegative integers(see Lamperti(1960)).

关键词： inhomogeneous biased random walk on the branching tree transience recurrence time-inhomogeneous branching process

Scaling limit theorem for transient random walk in random environment

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Frontiers of Mathematics in China 2018年第5期13卷 1033-1044页

作者： wenming hong Hui YANG School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China College of Science Minzu University of China Beijing 100081 China

We construct a sequence of transient random walks in random environments and prove that by proper scaling, it converges to a diffusion process with drifted Brownian potential. To this end, we prove a counterpart of co... 详细信息

关键词： Random walk random environment diffusion process Brownian motion with drift

Extremum of a time-inhomogeneous branching random walk

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Frontiers of Mathematics in China 2021年第2期16卷 459-478页

作者： Wanting HOU Xiaoyue ZHANG wenming hong Department of Mathematics Northeastern UniversityShenyang 110004China School of Statistics Capital University of Economics and BusinessBeijing 100070China School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems Beijing Normal UniversityBeijing 100875China

Consider a time-inhomogeneous branching random walk, generated by the point process Ln which composed by two independent parts: ‘branching’offspring Xn with the mean 1+B(1+n)−β for β∈(0,1) and ‘displacement’ ξn with a drift A(1+n)^(−2α) for α∈(0,1/2), where the ‘branching’ process is supercritical for B>0 but ‘asymptotically critical’ and the drift of the ‘displacement’ ξn is strictly positive or negative for |A|>0 but ‘asymptotically’ goes to zero as time goes to infinity. We find that the limit behavior of the minimal (or maximal) position of the branching random walk is sensitive to the ‘asymptotical’ parameter β and α.

关键词： Branching random walk time-inhomogeneous branching process random walk

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

Markov Processes and Related Topics(Ⅲ)

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Frontiers of Mathematics in China 2021年第2期16卷 255-256页

作者： wenming hong Yonghua MAO Yuhui ZHANG Research Center for Stochastics School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

It is our great pleasure to present the third special issue for the Markov Processes and Related Topics,on the occasion of the 20th anniversary of the Research Center for Stochastics of Beijing Normal University(BNU),supported by the innovative research group project of the National Natural Science Foundation of *** 2002,the Research Center for Stochastics started toorganize'Workshop on Markov Processes and Related Topics'.During the past 20 years,the workshop held almost each year except some special situations(for example,2003 SARS and 2020 COVID-19).Among the 16 workshops,11 of them were or will be co-organized with some universities out of Beijing。

关键词： China. Markov workshop

Light-tailed behavior of stationary distribution for state-dependent random walks on a strip

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Frontiers of Mathematics in China 2014年第4期9卷 813-834页

作者： wenming hong Meijuan ZHANG Yiqiang Q. ZHAO School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 China School of Statistics and Mathematics Central University of Finance and EconomicsBeijing 100081 China School of Mathematics and Statistics Carleton University Ottawa Ont K1S 5B6 Canada

We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.

关键词： Random walk on a strip stationary distribution light-tailedbehavior branching process recurrence state-dependent

THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 447-454页

作者： hong wenming(Institute of Mathematics, Fudan University Shanghai 200433, China) Institute of Mathematics Fudan University Shanghai 200433 China

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

关键词：分支率布朗时间冲突布朗运动占位时占位密度

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颞叶内侧胶质瘤的手术治疗策略分析

蚌埠医学院学报 2024年第7期49卷 862-865,869页

作者：李庆新吴炳山肖瑾陈为为洪文明王卫红徐培坤安徽医科大学第一附属医院神经外科安徽合肥230022

目的:依据颞叶内侧区解剖及各种辅助技术,探讨该区胶质瘤的手术切除策略与近期疗效。方法:回顾性分析手术切除的17例颞叶内侧区胶质瘤病人的临床资料,包括临床及影像学表现、术前评估、手术入路及技术要点、近期预后等情况。术前根据病... 详细信息

目的:依据颞叶内侧区解剖及各种辅助技术,探讨该区胶质瘤的手术切除策略与近期疗效。方法:回顾性分析手术切除的17例颞叶内侧区胶质瘤病人的临床资料,包括临床及影像学表现、术前评估、手术入路及技术要点、近期预后等情况。术前根据病人头颅多模态MRI成像指导手术入路和切除策略,术后早期复查头颅CT和MRI,出院前、术后1个月评价病人临床恢复情况。结果:根据术前评估结果采取改良颞前下入路12例、颞中回入路4例、颞上沟入路1例。肿瘤全切除15例(88.2%),次全切除2例(11.8%)。术后新发肢体活动障碍2例(合并感觉性失语1例)、动眼神经损伤1例,术后1个月随访上述症状均有改善;其余14例病人术后表现均较术前改善,无昏迷和死亡病人。结论:颞叶内侧区位置深在、解剖复杂,对其解剖结构的深入理解、采取合理的手术策略有助于该区胶质瘤的全切及病人神经功能保护,而多模态神经影像及术中神经导航技术的辅助价值较大。

关键词：颞叶内侧区胶质瘤手术策略多模态MRI 神经导航