New bounds for the first passage, wave-length and amplitude densities

Igor Rychlik

Stochastic Processes and their Applications, 1990, vol. 34, issue 2, 313-339

Abstract: 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 work, we have extended the formula to the case of processes which are smooth functions of a continuously differentiable Gaussian vector process. In the present paper we extend the results to more general kinds of first passage time problems, so called marked crossings, and use it to construct upper and lower bounds for the first passage, wave-length densities and for the transition distribution from a maximum to the following minimum. Numerical examples illustrate the results.

Keywords: crossings; *; fatigue; *; first; passage; density; *; marked; crossings; *; wave-height; *; wave-length (search for similar items in EconPapers)
Date: 1990
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