Date
Mon, 26 Nov 2007
Time
13:15 - 14:15
Location
Oxford-Man Institute
Speaker
Dr. John Moriarty
Organisation
Manchester

Reflected Brownian motion (RBM) in a two-dimensional wedge is a well-known stochastic process. With an appropriate drift, it is positive recurrent and has a stationary distribution, and the invariant measure is absolutely continuous with respect to Lebesgue measure. I will give necessary and sufficient conditions for the stationary density to be written as a finite sum of exponentials with linear exponents. Such densities are a natural generalisation of the stationary density of one-dimensional RBM. Using geometric ideas reminiscent of the reflection principle, I will give an explicit formula for the density in such cases, which can be written as a determinant. Joint work with Ton Dieker.

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