Large time and small noise asymptotic results for mean reverting diffusion processes with applications

Jeffrey Callen (), Lin Xu () and Suresh Govindaraj ()
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Jeffrey Callen: Stern School of Business, New York University, New York, NY 10012, USA
Lin Xu: School of Engineering, Princeton University, New Jersey, NJ 08554, USA
Suresh Govindaraj: Graduate School of Business, Columbia University, New York, NY 10027, USA

Economic Theory, 2000, vol. 16, issue 2, 419 pages

Abstract: We use the theory of large deviations to investigate the large time behavior and the small noise asymptotics of random economic processes whose evolutions are governed by mean-reverting stochastic differential equations with (i) constant and (ii) state dependent noise terms. We explicitly show that the probability is exponentially small that the time averages of these process will occupy regions distinct from their stable equilibrium position. We also demonstrate that as the noise parameter decreases, there is an exponential convergence to the stable position. Applications of large deviation techniques and public policy implications of our results for regulators are explored.

Keywords: Large deviations; Level-2-large deviations; Exit problems; Mean reverting stochastic differential equations. (search for similar items in EconPapers)
JEL-codes: C00 G10 (search for similar items in EconPapers)
Date: 2000-07-14
Note: Received: December 7, 1998; revised version: October 25, 1999
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Citations: View citations in EconPapers (3)

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