Multi-dimensional Brownian Motion with Darning

Speaker: 
Shuwen Lou
Date: 
Mon, Jun 18, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-MPrime Summer School in Probability
Abstract: 
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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