Mathematical Sciences: Brownian Motion and Diffusions

两位研究人员将继续他们在布朗运动方面的研究。主题将包括布朗运动和调和函数的边界行为，反映反射角度可变的布朗运动，布朗凸壳，布朗路径在区域边界上的行为，布朗运动的非马尔科夫方面，以及关于分数维的布朗运动。还将学习自我避免随机游走的另一个主题。两位研究人员将继续他们在布朗运动方面的研究。布朗运动是概率论研究的一种特殊的随机过程。这项研究将影响概率以外的数学领域，即位势理论和数学物理。

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.