GaDiFPT (version 1.0)

builtfunc: Functions characterizing the Gaussian Diffusion process X(t) and the considered threshold

Description

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).

Usage

a(t)
b(t)
cc(t)
S(t)
Sp(t)
a1(x, t) 
a2(t) 
mdt(t,y,tau)
vdt(t,tau) 
fdt(x,t,y,tau) 
psi (t, y, tau)

Arguments

x

current value of the process X(t)

t

current time

y

previous value of the process X at time tau

tau

previous time

Value

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

Examples

##---- 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')