Spectral Analysis of Brownian Motion with Jump Boundary
Abstract
Consider a family of probability measures
on a
bounded open domain with smooth boundary. For any
starting point , we run a standard -dimensional Brownian
motion until it first exits at time , at
which time it jumps to a point in the domain according to the
measure 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