Asymptotics and Evaluations of FPT Densities through Varying Boundaries for Gauss-Markov Processes

For Gauss-Markov processes the asymptotic behaviors of the first passage time probability density functions through certain time-varying boundaries are determined. Computational results for Wiener, Ornstein-Uhlenbeck and Brownian bridge processes show that for certain large boundaries and for large times excellent asymptotic approximations hold for such densities.