978-3-642-84789-9 Nonlinear Stochastic Mechanics 978-3-642-84791-2 residuals stochastic process lower dimension algorithm numerical algorithm https://scigraph.springernature.com/explorer/license/ 453-463 density analysis Slepian model random variables statistical applications transformation high accuracy approximation applications reliability numerical integration passage interest conditioning effective numerical algorithm accurate integral expressions small residuals chapter timedependent Rychlik accuracy approximation levels passage time package density FORTRAN subroutines first passage process behavior dimensions order en chapters first passage time behavior intelligent transformation time density passage time density level crossings false engineering model crossing time 1992 https://doi.org/10.1007/978-3-642-84789-9_39 approximation means process analysis subroutine regression approximation 2022-05-20T07:41 expression account Gaussian process First Passage and Wave Density Analysis by Means of the Computer Package CROSSREG central interest First passage times and intercrossing times for critical, constant or timedependent, levels are of central interest in reliability and many other engineering and statistical applications of stochastic processes. For Gaussian processes, very effective numerical algorithms can be constructed by means of Slepian models and regression approximations. A Slepian model is a process that describes the process behaviour conditioned on a level crossing. By conditioning on suitably chosen random variables one can obtain quite accurate integral expressions of low dimension, for the passage time density, simply by neglecting a small residual. The regression approximation has been systematically developed by Rychlik (1987). For an account of Slepian models and regression approximations, see Lindgren & Rychlik (1991). CROSSREG is a package of FORTRAN subroutines, which perform intelligent transformation and numerical integration in regression aprroximations in order to produce high accuracy approximations of the density of first passage and intercrossing times; see Rychlik & Lindgren (1990). variables integration integral expression 1992-01-01 Lindgren Igor Rychlik Springer Nature - SN SciGraph project Lindgren Georg Nicola Bellomo Mathematical Sciences Dept of Mathematical Statistics, Lund Institute of Technology, Box 118, S-221 00, Lund, Sweden Dept of Mathematical Statistics, Lund Institute of Technology, Box 118, S-221 00, Lund, Sweden Statistics pub.1009665274 dimensions_id Casciati Fabio Springer Nature doi 10.1007/978-3-642-84789-9_39