Iterated Brownian motion in an open set
Probability
2007-05-23 v1
Abstract
Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If \tau is the first exit time of iterated Brownian motion from the solid, then P(\tau>t) can be viewed as a measurement of the amount of contaminant left in the crack at time t. We determine the large time asymptotics of P(\tau>t) for both bounded and unbounded sets. We also discuss a strange connection between iterated Brownian motion and the parabolic operator {1/8}\Delta^2-\frac{\partial}{\partial t}.
Cite
@article{arxiv.math/0407137,
title = {Iterated Brownian motion in an open set},
author = {R. Dante DeBlassie},
journal= {arXiv preprint arXiv:math/0407137},
year = {2007}
}