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Sojourns and extremes of a diffusion process on a fixed interval

Published online by Cambridge University Press:  01 July 2016

Simeon M. Berman
Simeon M. Berman*
Affiliation:
New York University
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Abstract

Let X(t), , be an Ito diffusion process on the real line. For u > 0 and t > 0, let Lt (u) be the Lebesgue measure of the set . Limit theorems are obtained for (i) the distribution of Lt (u) for u → ∞and fixed t, and (ii) the tail of the distribution of the random variable max[0, t]X(s). The conditions on the process are stated in terms of the drift and diffusion coefficients. These conditions imply the existence of a stationary distribution for the process.

Keywords

DIFFUSION PROCESSLIMIT DISTRIBUTIONSOJOURNMAXIMUM VALUE

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 4 , December 1982 , pp. 811 - 832
Copyright
Copyright © Applied Probability Trust 1982 

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References

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