Description Usage Arguments Value Author(s) Examples
builtfunc
evaluates all the functions describing a generic Gaussian Diffusion process X(t) (drift, infinitesimal variance, mean, variance and first derivative of the transition density); it also evaluates the threshold function and its time derivative, both required in the evaluation of the kernel function of the Volterra integral equation for the FPT pdf (Buonocore 1987).
1 2 3 4 5 6 7 8 9 10 11 |
x |
current value of the process X(t) |
t |
current time |
y |
previous value of the process X at time tau |
tau |
previous time |
a1 |
gives the drift of the process as a(t)*x + b(t) |
a2 |
gives the infinitesimal variance of the process as cc(t) |
S |
gives the threshold |
Sp |
gives the threshold time derivative |
mdt |
gives the mean of the transition pdf of the process |
vdt |
gives the variance of the transition pdf of the process |
fdt |
gives the transition pdf of the process |
psi |
gives the kernel for evaluating the FPT pdf of the process via numerical integration of the Volterra integral equation |
A. Buonocore, M.F. Carfora
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ##---- Should be DIRECTLY executable !! ----
##-- ==> Define data, use random,
##-- or do help(data=index) for the standard data sets.
delta <- 0.5
time.vec <- seq(0, by=delta, 100)
# linear threshold
Scost <- 6
Sslope <- 0.2
# user provided function (see examples in demo folder)
SSS <- function(t) {
SSS <- Scost + Sslope*t
}
Slin <- S(time.vec)
plot(time.vec,Slin,type='l',xlab='time',ylab='threshold',main='linear threshold')
# periodic threshold
S0 <- 0
S1 <- 2
Sfr <- 0.5
# user provided function (see examples in demo folder)
SSS <- function(t) {
SSS <- S1*cos(Sfr*t+S0)
}
Sper <- S(time.vec)
plot(time.vec,Sper,type='l',xlab='time',ylab='threshold',main='periodic threshold')
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.