A Note on the Existence and Uniqueness of a Bounded Mean-Reverting Process

D Lesmono, , P Pollett, E Tonkes, K Burrage

Jounal of the Indonesian Mathematical Society, April 2009

Abstract

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

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