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Probability and Math Finance Seminar

Wenbo Li, University of Delaware

Spectral Analysis of Brownian Motion with Jump Boundary

Abstract

Consider a family of probability measures $\{\nu_y : y \in \partial D\}$ on a bounded open domain $D\subset \R^d$ with smooth boundary. For any starting point $x \in D$, we run a standard $d$-dimensional Brownian motion $B(t) \in \R^d $ until it first exits $D$ at time $\tau$, at which time it jumps to a point in the domain $D$ according to the measure $\nu_{B(\tau)}$ at the exit time, and starts the Brownian motion afresh. The same evolution is repeated independently each time the process reaches the boundary. The resulting diffusion process is called Brownian motion with jump boundary (BMJ). There are various motivating applications for the study of the BMJ process, also called rebirth process, including the double knock-out barrier options in derivative markets. The spectral gap of non-self-adjoint generator of BMJ, which describes the exponential rate of convergence to the invariant measure, is studied.

MONDAY, November 17, 2008
Time: 5:00 P.M.
Location: WeH 6423