Wenbo V. Li
Title: Diffusions with holding and jumping boundary
Co-Authors: Jun Peng
Abstract:
Consider a family of probability measures $\{\nu_\xi\}$ on a bounded open region $D\subset \R^d$ with
a smooth boundary and a positive parameter set $\{\beta_\xi\}$, all
indexed by $\xi \in\partial D$. For any starting point inside $D$,
we run a diffusion until it first exits $D$, at which time it stays
at the exit point $\xi$ for an independent exponential holding time
with rate $\beta_{\xi}$ and then leaves $\xi$ by a jump into $D$
according to the distribution $\nu_{\xi}$. Once the process jumps
inside, it starts the diffusion afresh. The same evolution is
repeated independently each time the process jumped into the domain
and the resulting Markov process is called diffusion with holding
and jumping boundary (DHJ).
In this paper we provide a study of DHJ which is not reversible due to jumping, on its
generator, stationary distribution and the speed of convergence.
Corrections:
Updated relevant references:
Last modified Oct. 10, 2010 by Wenbo V. Li,
wli@math.udel.edu