부산대학교 도서관

We study the following "inverse first passage time" problem. Given a diffusion process Xt and a probability distribution q on [0,∞), does there exist a boundary b(t) such that q(t) = P[τ ≤ t], where τ is the first hitting time of Xt to the time-dependent level b(t)? A free boundary problem for a parabolic partial differential operator is associated with the inverse first passage time problem. We prove the existence and uniqueness of a viscosity solution to this problem. We also investigate the small time behavior of the boundary b(t), presenting both upper and lower bounds. Finally, we derive some integral equations characterizing the boundary. [ABSTRACT FROM AUTHOR]