by Lehmann, A..
Series: 1996-16, Preprints
t X T be a one-dimensional Markov process with
continuous sample paths. We investigate continuity and differ-
entiability properties of first passage time (FPT) distributions of
X T with respect to continuous upper and lower moving bound-
aries. Using Volterra-Stieltjes integral equation techniques we
give sufficient conditions for Hölder continuity of the FPT distri-
bution function and the existence of a FPT density. We discuss
our results for Brownian motion and its nonrandom Markovian
transforms, in particular, for the Ornstein-Uhlenbeck process.
First passage time, Moving boundaries, Markov processes, Brownian motion process, Ornstein-Uhlenbeck process, Integral equation