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

D. Lesmono, P.K. Pollet, E.J. Tonkes, K. Burrage


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


Keywords


Stochastic differential equation, mean-reverting diffusions, boundary behaviour

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p-ISSN:2086-8952e-ISSN:2460-0245