# h.fn.exp: Mean Intensity of the Self-Exciting Point Process With an... In IHSEP: Inhomogeneous Self-Exciting Process

h(t)=ν(t)+\int_0^t g(t-s)h(s)ds, t≥q 0

, where the excitation function is exponential: g(t)= γ_1 e^{-γ_2 t}.

## Description

Mean Intensity of the Self-Exciting Point Process With an Exponential Excitation Function h.fn.exp calculates the mean intensity function h(t) which solves the integral equation

h(t)=ν(t)+\int_0^t g(t-s)h(s)ds, t≥q 0

, where the excitation function is exponential: g(t)= γ_1 e^{-γ_2 t}.

## Usage

 1 h.fn.exp(x, nu, g.p = c(4, 8)) 

## Arguments

 x numerical scalar, at which the mean intensity h is to be evaluated nu a function, which gives the baseline event rate g.p a numeric vector of two elements giving the two parameters γ_1,γ_2 of the exponential excitation function

## Value

a numric scalar which gives the value of the function h at x.

h.fn

## Examples

 1 2 3 4 5 6 nu <- function(x)200+100*cos(pi*x); x <- 1:500/100; y <- sapply(x,h.fn.exp,nu=nu,g.p=c(2,1)); h <- splinefun(x,y); g <- function(x)2*exp(-x) round(nu(x)+sapply(x,function(x)integrate(function(u)g(x-u)*h(u),0,x)\$value) - y,5) 

### Example output

  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[186] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[223] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[260] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[297] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[334] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[371] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[408] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[445] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[482] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


IHSEP documentation built on Aug. 16, 2021, 5:07 p.m.