Mathematical Sciences: Brownian Motion and Diffusions

两位研究人员将继续在以下方面进行研究 布朗运动。 主题将包括布朗运动和 调和函数的边界行为，反映布朗 变反射角运动，布朗凸 船体，区域边界上布朗路径的行为， 布朗运动的非马尔可夫侧，以及 分形 自避免随机游走的另一个主题将 被研究。 两位研究人员将继续在以下方面进行研究 布朗运动。 布朗运动是一种特殊的随机 概率论中研究的过程。 本研究将 概率之外的数学影响领域，即潜在的 理论和数学物理。

The two investigators will continue their studies in aspects of Brownian motion. Topics will include Brownian motion and the boundary behavior of harmonic functions, reflecting Brownian motion with variable angle of reflections, the Brownian convex hull, behavior of Brownian paths on the boundary of a domain, the non-Markovian side of Brownian motions, and Brownian motion on fractals. An additional topic of self-avoiding random walk will be studied. The two investigators will continue their studies in aspects of Brownian motion. Brownian motion is a specific stochastic process which is studied in probability theory. This study will impact areas of mathematics outside probability, namely potential theory and mathematical physics.