Cauchy退火的收敛性问题 *

证明了在相当广泛的情形下,Cauchy退火不能够依概率收敛到整体最小.     

完备可分度量群上的齐次Levy过程的复合Poisson逼近

该文利用算子半群的方法给出了取值于具有左不变度量的完备可分群的齐次Levy过程是复合Poisson过程的弱极限这一结论．     

环面上具有间断梯度的势函数的模拟退火

本文证明了环面上具有间断梯度的势函数的模拟退火过程：dXt=-VU(Xt)dt √2dWt概率收敛到势函数的全局极小集附近。     

THE FINITE INVARIANT MEASURES AND THE REVERSIBLE MEASURES OF THE DIFFUSIONS WITH THE VENTZEL''''S BOUNDARY CONDITIONS IN THE CIRCULAR DISC

For a given rotation-invariant operator Ω in the unit disc, the necessary condition for thef xistence of finite invariant measures of the strong Markov transition functions determined by Ω with the Ventzel's boundary conditions of finite rank is established If only rotation-invariant transition functions are considered, then the necessary and sufficient conditions for a given measure to be invariant and to be reversible, and all the cor6esponding boundary conditions for posseusiug these properties have been found explicitly in this paper.     

ON THE LARGE DEVIATION FUNCTIONS OF MARKOV CHAINS

In this paper, we consider that how much information the large deviation rate functions contain. Namely, let us observe two processes Ⅹ~(1) and Ⅹ~(2) with the same large deviation function Ⅰ(μ), for all μ with compact support, and ask what the relation should have between Ⅹ~(1) and Ⅹ(~). In [1], Donsker and Varadhan gave the answer for the case of diffusion as the following theorem.     

非紧Riemann流形上平稳扩散过程的熵产生率

给出了具有有界Nelson速度流的平稳扩散过程的熵产生率的封闭形式,讨论了一列反射扩散的熵产生率的极限。     

正常返漂移布朗过程的角特征

在本文中,我们讨论了正常返带漂移的布朗运动的角特征的渐近行为,指出了存在两个常数C_1,C_2,使在弱收敛意义下,有φt/t→C_1ζ c_2(t→∞),这里ζ是一个哥西随机变量,并且当过程对称时c_2=0。     

有限不变测度与一维扩散过程

<正> 本文沿用[2]或[3]中的记号. 对于微分算符Ω: Ωu=(a(x)u′)′+b(x)u′+c(x)u(1) a(x)>0,c(x)≤0,a(x),b(x)连续可微,c(x)连续以及它的形式共轭算符Ω: Ωv=(a(x)v′)′-(b(x)v)′+c(x)v(2)我们将说明:在c(x)0时Ω导出的满足局部边值条件的马氏过程P(t,x,Γ)(确切含义见[2]或[3]中定义4.5.1,4.5.4及4.5.5)不存在有限不变测度;在c(x)≡0时Ω导出的满足局部边值条件的马氏过程P(t,x,Γ)如果存在有限不变测度,则必是绝对连续的且其密度满足共轭方程.     

ON THE STATISTICAL MECHANICS OF PROBABILISTIC MODELS OF NEURAL NETWORKS

ＯＮＴＨＥＳＴＡＴＩＳＴＩＣＡＬＭＥＣＨＡＮＩＣＳＯＦＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＯＤＥＬＳＯＦＮＥＵＲＡＬＮＥＴＷＯＲＫＳＱＩＡＮＭＩＮＰＩＮＧ（钱敏平）（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＢｅｉｊｉｎｇＵ...     

流形上半鞅线积分与半鞅互变差的注记

给出了两流形上半鞅的互变差。