Large Time and Small Noise Asymptotic Results for Mean Reverting Diffusion Processes with Applications

Posted: 8 Nov 2000

See all articles by Jeffrey L. Callen

Jeffrey L. Callen

University of Toronto - Rotman School of Management

Suresh Govindaraj

Rutgers University - Rutgers Business School - Newark and New Brunswick

Lin Xu

Princeton University - School of Engineering and Applied Science

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

JEL Classification: C00, G10

Suggested Citation

Callen, Jeffrey L. and Govindaraj, Suresh and Xu, Lin, Large Time and Small Noise Asymptotic Results for Mean Reverting Diffusion Processes with Applications. Economic Theory, Vol. 16, Issue 2. Available at SSRN: https://ssrn.com/abstract=236695

Jeffrey L. Callen

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada
416-946-5641 (Phone)
416-971-3048 (Fax)

Suresh Govindaraj (Contact Author)

Rutgers University - Rutgers Business School - Newark and New Brunswick ( email )

1 Washington Park
Room #934
Newark, NJ 07102
United States

Lin Xu

Princeton University - School of Engineering and Applied Science ( email )

Princeton, NJ 08554

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