Complete asymptotic decomposition of the sojourn probability of a diffusion process in thin domains with moving boundaries

We investigate a diffusion process ξ(t) with absorption defined in a thin domainD _ε ={(x,t)∶εG ₁ (t) ₂ (t), t≥0}. We obtain the complete decomposition of the sojourn probability of ξ(t) inD _ε with respect to ε→0. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1155–1164, September, 1999.