builtfunc: Functions characterizing the Gaussian Diffusion process X(t)...

In GaDiFPT: First Passage Time Simulation for Gaussian Diffusion Processes

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

Author(s)

A. Buonocore, M.F. Carfora

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')

GaDiFPT documentation built on May 2, 2019, 1:18 p.m.