In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.
"Parisian ruin of self-similar Gaussian risk processes." J. Appl. Probab. 52 (3) 688 - 702, September 2015. https://doi.org/10.1239/jap/1445543840