setPpr: Point Process

In yuima: The YUIMA Project Package for SDEs

Point Process

Description

Constructor of a Point Process Regression Model

Usage

setPPR(yuima, counting.var = "N", gFun, Kernel,
  var.dx = "s", var.dt = "s", lambda.var = "lambda",
  lower.var = "0", upper.var = "t", nrow = 1, ncol = 1)

Arguments

yuima	an object of yuima.model-class that describes the mathematical features of counting and covariates processes Y[t]=(X[t],N[t]).
counting.var	a label denoting the name of the counting process.
gFun	a vector string that is the mathematical expression of the vector function g(t,Y[t-],theta) in the intensity process.
Kernel	a matrix string that is the kernel kappa(t-s,Y[s],theta) in the definition of the intensity process.
var.dx	a string denoting the integration variable in the intensity process.
var.dt	a string denoting the integration time variable in the intensity process.
lambda.var	name of the intensity process.
lower.var	Lower bound of the support for the integral in the definition of the intensity process.
upper.var	Upper bound of the support for the integral in the definition of the intensity process.
nrow	number of rows in the kernel.
ncol	number of columns in the kernel.

Value

An object of yuima.PPR

Note

There may be missing information in the model description. Please contribute with suggestions and fixings.

Author(s)

The YUIMA Project Team

Contacts: Lorenzo Mercuri [e-mail]

References

Insert Here References

Examples

## Not run: 
## Hawkes process with power law kernel

# I. Law Definition:
my.rHwk2 <- function(n){
  as.matrix(rep(1,n))
  }
Law.Hwk2 <- setLaw(rng = my.rHwk2, dim = 1)

# II. Definition of the counting process N_t
mod.Hwk2 <- setModel(drift = c("0"), diffusion = matrix("0",1,1),
  jump.coeff = matrix(c("1"),1,1), measure = list(df = Law.Hwk2),
  measure.type = "code", solve.variable = c("N"),
  xinit=c("0"))

# III. Definition of g() and kappa()
g.Hwk2 <- "mu"
Kern.Hwk2 <- "alpha/(1+(t-s))^beta"

# IV. Construction of an yuima.PPR object
PPR.Hwk2 <- setPPR(yuima = mod.Hwk2, gFun=g.Hwk2,
  Kernel = as.matrix(Kern.Hwk2),var.dx = "N")

## End(Not run)

yuima documentation built on Dec. 28, 2022, 2:01 a.m.