The two-barrier problem for continuously differentiable processes
- 1 March 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 24 (01) , 71-94
- https://doi.org/10.1017/s0001867800024174
Abstract
An efficient algorithm to compute upper and lower bounds for the first-passage time in the presence of a second absorbing barrier by means of a continuously differentiable decomposable process, e.g. a smooth function of a continuously differentiable Gaussian vector field, is given. The method is used to obtain accurate approximations for the joint density of the zero-crossing wavelength and amplitude and the distribution of the rainflow cycle amplitude. Numerical examples illustrating the results are also given.Keywords
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