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.
"Extreme analysis of a random ordinary differential equation." J. Appl. Probab. 51 (4) 1021 - 1036, December 2014.