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Extreme Analysis of a Random Ordinary Differential Equation

Part of: Limit theorems

Published online by Cambridge University Press:  30 January 2018

Jingchen Liu  and
Xiang Zhou
Jingchen Liu*
Affiliation:
Columbia University
Xiang Zhou*
Affiliation:
City University of Hong Kong
*
∗ Postal address: Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY 10027, USA. Email address: [email protected]
∗∗ Postal address: Y6524 (Yellow Zone), 6/F Academic 1, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong.
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Abstract

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In this paper we consider a one dimensional stochastic system described by an elliptic equation. A spatially varying random coefficient is introduced to account for uncertainty or imprecise measurements. We model the logarithm of this coefficient by a Gaussian process and provide asymptotic approximations of the tail probabilities of the derivative of the solution.

Keywords

Random differential equationextremesrare event

MSC classification

Primary: 60F10: Large deviations
Secondary: 65Z05: Applications to physics
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 1021 - 1036
Copyright
© Applied Probability Trust 

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