Mathematical Sciences: Brownian Motion and Related Stochastic Processes

首席研究员和他的合作者马克·约尔将继续他目前对随机过程的研究，特别是布朗运动和相关过程。注意力将集中在可以用鞅微积分、局部时间和偏移理论来处理的问题上。具体的研究课题如下：与从属子相关的区间划分，2维和3维布朗运动的多点，离散时间的Tsirelson方程，布朗运动的非正则分解，Ciesielski-Taylor恒等式，稳定指标（1/2）变量的多元柯西变量和仿射分解，马尔可夫过程的缠结，布朗滤波的表征。首席研究员和他的合作者马克·约尔将继续他目前对随机过程的研究，特别是布朗运动和相关过程。注意力将集中在可以用鞅微积分、局部时间和偏移理论来处理的问题上。随机过程是概率论中一个重要的研究领域。

The principal investigator, together with his collaborator Marc Yor, will continue his present lines of research into stochastic processes, particularly Brownian motion and related processes. Attention will be focussed on problems amenable to treatment using the tools of martingale calculus, local time and excursion theory. Particular subjects for study are the following: interval partitions associated with a subordinator, multiple points of Brownian motion in dimensions 2 and 3, Tsirelson's equations in discrete time, non-canonical decompositions of Brownian motion, the Ciesielski-Taylor identities in law, multivariate Cauchy variables and affine decompositions of a stable variable of index (1/2), intertwinings of Markov processes, and characterization of the Brownian filtration. The principal investigator, together with his collaborator Marc Yor, will continue his present lines of research into stochastic processes, particularly Brownian motion and related processes. Attention will be focussed on problems amenable to treatment using the tools of martingale calculus, local time and excursion theory. Stochastic processes represent an important area of research in probability theory.