96-16
Hölder Continuity and Differentiability of First Passage Time Distributions for Continuous Markov Processes
by Lehmann, A.
Preprint series: 96-16, Preprints
- MSC:
- 60J25 Markov processes with continuous parameter
- 60J65 Brownian motion, See also {58G32}
- 60G40 Stopping times; optimal stopping problems; gambling theory, See also {62L15, 90D60}
Abstract: Let X T be a one-dimensional Markov process withcontinuous sample paths. We investigate continuity and differ-entiability properties of first passage time (FPT) distributions ofX T with respect to continuous upper and lower moving bound-aries. Using Volterra-Stieltjes integral equation techniques wegive sufficient conditions for Hlder continuity of the FPT distri-bution function and the existence of a FPT density. We discussour results for Brownian motion and its nonrandom Markoviantransforms, in particular, for the Ornstein-Uhlenbeck process.
Keywords: First passage time, Moving boundaries, Markov processes, Brownian motion process, Ornstein-Uhlenbeck process, Integral equation