A NOTE ON THE EXISTENCE AND UNIQUENESS OF A BOUNDED MEAN-REVERTING PROCESS

Abstract

We study a stochastic differential equation (SDE) describing a class of mean-reverting diffusions on a bounded interval. The drift coefficient is not continuous near theboundaries. Nor does it satisfy either of the usual Lipschitz or linear growth conditions.We characterize the boundary behaviour, identifying two possibilities: entrance boundaryand regular boundary. In the case of an entrance boundary we establish existence anduniqueness of the solution to the SDE.

DOI : http://dx.doi.org/10.22342/jims.14.2.53.83-94