IHSEP (version 0.3.1)

simHawkes1: Simulate a Hawkes process, or Self-exciting point process

Description

Simulate an (inhomogeneous) self-exciting process with given background intensity and excitation/fertility function.

Usage

simHawkes1(nu=NULL, g=NULL, cens = 1,
           nuM=max(optimize(nu,c(0,cens),maximum=TRUE)$obj, nu(0), nu(cens))*1.1,
           gM=max(optimize(g,c(0,cens),maximum = TRUE)$obj, g(0),
g(cens))*1.1,
           exp.g=FALSE,gp=c(1,2))

Value

A list of vectors of arrival/birth times of individuals/events of generations 0, 1, ... The length of the list is the total number of generations.

Arguments

nu

A (vectorized) function. The baseline intensity function.

g

A (vectorized) function. The excitation function.

cens

A scalar. The censoring time, or the time of termination of observations.

nuM

A scalar. The maximum time of the baseline intensity from 0 to cens.

gM

A scalar. The maximum time of the excitation function from 0 to cens.

exp.g

A logical. Whether the excitation function g should be treated as an exponential function.

gp

A vector of two elements, giving the two parameters a and b in the exponential excitation function \(g(x)=a*exp(-b*x)\), which is used when exp.g is set to TRUE, and is ignored otherwise.

Author

Feng Chen <[e-mail]>

Details

The function works by simulating the birth times generation by generation according to inhomegenous Poisson processes with appropriate intensity functions (\(\nu\) or \(g\)).

See Also

simHawkes0

Examples

  asepp <- simHawkes1(nu=function(x)200*(2+cos(2*pi*x)),nuM=600,
                      g=function(x)8*exp(-16*x),gM=8)