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