Multi-dimensional Brownian Motion with Darning

PIMS-MPrime Summer School in Probability

授课人:Shuwen Lou

机构:Pacific Institute for the Mathematical Sciences(PIMS)

关键词: Scientific;    Mathematics;    Probability;    Brownian Motion;   

加拿大|英语

【 摘 要 】

The reason that we define multi-dimensional Brownian motion as a darning process is that, even for the simplest case which is R^2 being unioned with R^1, such a process cannot be defined in the usual sense, because 2-dimensional Brownian motion never hits a singleton. Constructions of darning processes are based on one-point extension theory which was first studied by M. Fukushima. Lots of very interesting examples, for instance, circular Brownian motion, Brownian motion with a ``knot", etc., can be constructed in this way, some of which will be provided in the talk. The rest of the talk will be focusing on the heat kernel estimates of multi-dimensional Brownian motion with darning.

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