Two Barriers Problem for Continuously Differentiable Processes
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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Durbin has presented a compact formula for the first passage density of a Gaussian process, which is locally like Brownian motion, to a smooth barrier. In previous works, we have extended the formula to the case of processes which are smooth functions of a continuously differentiable Gaussian vector process and to more general kinds of first passage time problems, so called marked crossings. In the present paper we obtain similar results for the first passage density in presence of a second absorbing barrier and use it to construct upper and lower bounds for the first passage, rainflow cycle amplitude, zerocrossing wave-length and amplitude densities. Numerical examples illustrate the results.
- Statistics and Probability