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

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

doi:10.22342/jims.14.2.53.83-94

D. Lesmono ⁽¹⁾ , P.K. Pollet ⁽²⁾ , E.J. Tonkes ⁽³⁾ , K. Burrage ⁽⁴⁾

(1) Department of Mathematics, Universitas Katolik Parahyangan, Bandung 40141, Indonesia., Indonesia,

(2) Department of Mathematics, The University of Queensland, Brisbane, Australia., Australia,

(3) Energy Edge Pty, Ltd., Brisbane, Australia., Australia,

(4) Institute for Molecular Bioscience, The University of Queensland, Brisbane, Australia., Australia

https://doi.org/10.22342/jims.14.2.53.83-94

Issue
Volume 14 Number 2 (October 2008)

Submitted
May 11, 2012

Accepted
June 2, 2012

Published
June 2, 2012

Keywords:

Stochastic differential equation, mean-reverting diffusions, boundary behaviour

No galleys available

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

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Authors

D. Lesmono

Department of Mathematics, Universitas Katolik Parahyangan, Bandung 40141, Indonesia.

penulis@jims-a.org (Primary Contact)

P.K. Pollet

Department of Mathematics, The University of Queensland, Brisbane, Australia.

E.J. Tonkes

Energy Edge Pty, Ltd., Brisbane, Australia.

K. Burrage

Institute for Molecular Bioscience, The University of Queensland, Brisbane, Australia.

Author Biography

P.K. Pollet, Department of Mathematics, The University of Queensland, Brisbane, Australia.

Lesmono, D., Pollet, P., Tonkes, E., & Burrage, K. (2012). A NOTE ON THE EXISTENCE AND UNIQUENESS OF A BOUNDED MEAN-REVERTING PROCESS. Journal of the Indonesian Mathematical Society, 14(2), 83–94. https://doi.org/10.22342/jims.14.2.53.83-94