##### Department of Mathematics,

University of California San Diego

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### Probability Seminar

## Patrick Fitzsimmons

#### UCSD

## Brownian Motion in Three Dimensions Conditioned to have the Origin as a Recurrent Point

##### Abstract:

Last February, Mike Cranston spoke in this Seminar about a polymer model based on three-dimensional Brownian motion conditioned to hit (and keep returning to) the origin. I will discuss the construction and certain properties of this conditioned Brownian motion from two points of view (i) Dirichlet forms, and (ii) excursion theory. The latter gives a nice interpretation of the Johnson-Helms example from martingale theory. It turns out that this diffusion process is not a semimartingale, even though its radial part is just a one-dimensional Brownian motion reflected at the origin. Based on joint work with Liping Li of Fudan University.

### December 4, 2014

### 9:00 AM

### AP&M 6402

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