Abstract
A detailed study of first- and second-order approximations to the first passage time conditional probability density function (p.d.f.) of a stationary Gaussian process with differentiable sample paths is provided both theoretically and numerically. An evaluation of mode and peak value of this function is also given and asymptotic expressions are derived for the functions W n ( t 1, t 2, …, t n |; x 0) ( n ⩾ 1) appearing in the series expansion of the first passage time probability density function.
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