First-passage problems for jump-diffusion processes

Let {X(t), t ≥ 0} be a diffusion process with jumps according to a Poisson process, and let τ (x) be the first time that the process, starting from X(0) = x, leaves the interval (a, b). Various problems for which the continuous part of the process is a Wiener, Ornstein-Uhlenbeck or Bessel process are considered. The jumps are distributed uniformly and are x-dependent. Exact and explicit expressions are obtained by solving integro-differential equations, subject to the appropriate boundary conditions.