Mathematical Sciences: Research in Stochastic Processes

这三个一般的研究领域是流形上的布朗运动、测值过程和随机游动的范围。其中一个统一的主题是交叉点地方性研究。这项研究是研究者以前所得到的结果的推广。使用当地时间的各种形式的交叉点。由于最近发现了平稳高斯过程样本连续的充要条件，促进了对Levy过程局部时的研究。高阶交集局部时的正则部分的分离导致了预期被积函数的研究。为这些被积分器开发的各种新方法将有助于高阶交集本地时的研究。

The three general areas of research are Brownian motion on manifolds, measure valued processes, and the range of a random walk. The unifying theme among them is the study of intersection local times. The research is generalization to manifolds of the results previously obtained by the investigator. Various forms of intersection local times are used. Study of the local times for Levy processes is prompted due to the relatively recent discovery of the necessary and sufficient condition for sample continuity of a stationary Gaussian process. The isolation of the regular part of the intersection local times of higher orders lead in a normal way to the study of anticipative integrands. Various new methods developed for these integrands will contribute towards the study of the higher order intersection local times.