##### Department of Mathematics,

University of California San Diego

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### Probability Seminar

## Ron Getoor

#### UCSD

## Walsh's interior reduite

##### Abstract:

This will be an expository talk. I'll begin by introducing the concepts of reduite (reduced function) and balayage (swept measure) in classical potential theory and their interpretations in terms of Brownian motion. I'll then discuss the extension of these ideas to Markov processes as in Hunt's fundamental memoir. After introducing h-transforms I'll be able to define the interior reduite and discuss some of its properties following Walsh. If time permits I'll give some indications of recent work in this area by Fitzsimmons and myself.

### April 19, 2007

### 10:00 AM

### AP&M 6402

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