Ergodic theorem for the two-dimensional super-Brownian motion with super-Brownian immigration

By investigating the related nonlinear equation, the ergodic theorem is obtained for the super-Browni-an with super-Brownian immigration in two dimension.     

RESEARCH NOTES On the support of super-Brownian motion with super-Brownian immigration

The support properties of the super Brownian motion with random immigration Xρ1 are considered,where the immigration rate is governed by the trajectory of another super-Brownian motion ρ. When both the initial state Xρo of the process and the immigration rate process ρo are of finite measure and with compact supports, the probability of the support of the process Xρi dominated by a ball is given by the solutions of a singular elliptic boundary value problem.     

Central limit theorem for the occupation time of catalytic super-Brownian motion

The catalytic super_Brownian motion has been considered. If both the catalytic medium process Q and CSBM started with Lebesgue measure λ, the central limit theorem for occupation time of CSBM has been obtained in dimension 3 for P-λ_a.s.Q.     

Limit theorems for the weighted occupation time for super-Brownian motions on Hd

Weighted occupation time processes associated with the super-Brownian motions on hyperbolic spaces are investigated. Longtime behavior and a central limit type theorem for the processes are obtained. For all dimension d≥2, the right normings for two fluctuations are t and t^1/2, and the limit results are the Riemannian measure and some centered Gaussian random measure, respectively.     

Opial条件下渐近非扩张型半群殆轨道的遍历定理

X是-Banach空间,(X,τ)是局部凸线性拓扑空间,C是X上的τ-序列紧凸集,S是C上的Γ类渐近非扩张型半群.首先给出了局部一致τ-Opial条件的概念,运用乘积拓扑网技巧得到了具有局部一致τ-Opial条件下空间X的新的收敛条件.然后利用该收敛条件得到了在局部一致τ-Opial条件下的,类渐近非扩张型半群殆轨道的遍历定理以及τ-收敛定理.结论是将已有结果由一致τ-Opial条件推广到局部一致τ-Opial条件,对空间X的要求进一步减弱,该结论是遍历定理在非一致凸空间中的延伸.     

Limit theorems for the weighted occupation time for super-Brownian motions on Hd

Weighted occupation time processes associated with the super-Brownian motions on hyperbolic spaces are investigated. Longtime behavior and a central limit type theorem for the processes are obtained. For all dimension d≥2, the right normings for two fluctuations are t and t^1/2, and the limit results are the Riemannian measure and some centered Gaussian random measure, respectively.     

Limit theorems for the weighted occupation time for super-Brownian motions on H~d

Weighted occupation time processes associated with the super-Brownian motions on hyperbolic spaces are investigated. Longtime behavior and a central limit type theorem for the processes are obtained. For all dimension d≥2, the right normings for two fluctuations are t and t1/2 , and the limit results are the Riemannian measure and some centered Gaussian random measure, respectively.     

临界超布朗运动的遍历定理

考虑以Ｌｅｂｅｓｇｕｅ测度μ为初值的Ｍｐ（Ｒ＾ｄ）－值超布朗运动,其分枝特征为ψ（ｘ,ｚ）＝－（１＋│ｘ│＾θ２２（－２〈≤－１）若底空间维数ｄ＝１它的全占位时无穷,同时,强遍达历定理成立。     

有关迭代函数系统遍历性质的推广

研究无穷迭代函数系统的遍历性质.利用Banach极限原理、Riesz表现定理及数学归纳法,对紧度量空间上无穷迭代函数系统的遍历定理进行推广,得到了无穷迭代函数系统推广的遍历定理.     

随机环境中马氏过程的强遍历性及收敛速度

文章引进随机环境中马氏过程的模型,研究了该模型的马氏过程满足强遍历性的各种充要条件;证明了当随机转移函数P（θ^·[s,s＋t）;x,A）属于G^＋时,强遍历性蕴含了收敛的指数速度;找出了最佳收敛速度;并得到了达到最佳收敛速度的条件．     

一个两状态平稳遍历马尔可夫链部分和序列最小值分布的精确尾估计

一般情况下对平稳遍历马尔可夫链部分和序列最小值分布进行精确尾估计是较困难的，利用条件全概率公式，并通过求解差分方程．给出两状态情况下一个精确尾估计的具体表达式。     

倒向随机微分方程第二部分解的比较定理

为研究倒向随机微分方程第二部分解的比较性质,利用倒向随机微分方程解的Malli-avin微分,第二部分解可化为一个线性倒向随机微分方程的第一部分解,再结合经典的比较定理,给出第二部分解的比较定理成立的一个充分条件。通过该比较定理,可以把第二部分解控制在一个确定的闭区间,并由此指出一类可以退化为常微分方程的倒向随机微分方程。     

生成元为左Lipschitz的倒向随机微分方程最大解的Levi型定理

证明了生成元为左Lipschitz的一维倒向随机微分方程最大解的Levi型定理。     

适于配送车辆导航路径规划的遍历模型的改进型粒子群优化算法

车辆路径规划是物流配送导航系统中的关键环节,是实现物流配送路径引导的前提条件和车辆导航的技术保障.为解决物流配送车辆导航中的路径规划问题,文中建立了物流配送车辆导航路径规划(VND)遍历模型,设计了求解该模型的改进型粒子群算法,并对初始种群的产生方法及种群的进化策略进行改进,使原本不能直接用于求解VND模型的基本粒子群...     

关于微分方程局部解存在定理证明的注记

通过对有关微分方程局部解存在定理经典证明的研究,给出了一个强化条件下的局部解存在定理,同时给出了一个一阶常微分方程解存在的简化证明和解的一般表达式,并提出教学建议。     

一维波动方程的对顶点定理

证明了无限长弦的振动方程的解满足对顶点定理,利用该定理求解了古尔沙问题和达布问题．     

均匀磁场中辐射电子的阻尼运动

介绍了均匀磁场中计算辐射阻尼影响时相对论电子协变运动方程的一种解析求解方法.在场强约束条件γB 9×1011T下导出了电子运动的初级近似解和相应的同步辐射能量损失率的表达式.最后,简单讨论了所得结果的适用性和量子效应对运动解精度的可能影响.     

Disturbance evolution and the nonlinear stability to the basic flows for two-dimensional quasi-geostrophic motion

The status of disturbances of both initial values and parameters in the models is further investigated, the exact explicit estimates on the disturbance energy and disturbance potential enstrophy are given; and while the initial disturbance fields rely only on the initial disturbance potential enstrophy, initial disturbance velocity circulation along the boundary, disturbance parameters, and the nonlinear stability criteria paralleling to Arnold’s second theorem are obtained, and the main results of Mu are generalized.