The paper studies first exit times from domains for diffusion processes and their dependence on variations of the boundary. We establish some robustness of the first exit times with respect to the fluctuations of the boundary. More precisely, we present an estimate of the $L_1$-distance between exit times from two regions via expectations of exit times.
"On the dependence of the first exit times on the fluctuations of the domain boundary." Electron. Commun. Probab. 20 1 - 3, 2015. https://doi.org/10.1214/ECP.v20-4531