一类奇异情形的测度值过程

构造了一类描述在R^d中测度如何在随机流或``虚流''''下演化的测度值过程. 一方面可视此类过程为测度值流, 另一方面已有的可测映射流、核的流的框架不能覆盖此类过程.     

路径空间上的拟不变曲线

对Li提出的关于负Markov联络是否存在惟一的拟不变测地线问题给出了肯定的回答.     

拟顶点可迁图上简单随机游走的切割点

证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.     

(α,d,β)超过程Tanaka公式的注记

在最优的初始条件及最优的维数条件下, 证明了(α,d,β)超过程关于局部时的Tanaka公式成立.     

连续环群的Ricci形式

本文给出了连续环群的Ricci形式是闭的充分必要条件．     

Quasi-invariant transformations on the path space over a manifold

Some interesting quasi-invariant transformations on the path space over a Riemannian manifold are investigated. The results improve some previous ones. An erratum to this article is available at .     

DISCUSSIONS ON HEAT KERNEL MEASURE AND PINNED WIENER MEASURE

1. IntroductionThe log-Sobolev inequalities on loop spaces over compact Riemannian manifolds havebeen received much attention (see [1-6]). In particular, for loop group over a compact typeLie group, by replacing pinned Wiener measure with a heat kernel measure, Driver andLohrenz[2] obtained a log-Sobolev inequality without added potential.Let G be a d-dimensional compact type Lie group with unit element e and harr measuredx. Denote by g the Lie algebra of G with an Ad(G) invariant inner …     

流形上的随机和乐

对路径空间上的OU过程, 计算了沿着它的环的随机和乐. 所得结果表明得到的随机和乐恰好给出Markov联络沿OU过程的平行移动.     

Parallel transports associated to stochastic holonomies

A stochastic holonomy along a loop obtained from the OU process on the path space over a compact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives the parallel transport with respect to the Markov connection along the OU process on the path space     

A REMARK ON A BMO MARTINGALE

Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p II[E[IMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply …