yuima.carmaHawkes-class function

Class for the mathematical description of a Hawkes process with a CARMA(p,q) intensity

The yuima.carmaHawkes class is a class of the yuima package that extends the yuima.model-class. class

Slots

• info:: is an carmaHawkes.info-class object that describes the structure of the CARMA(p,q) model.

• drift:: is an expression which specifies the drift coefficient (a vector).

• diffusion:: is an expression which specifies the diffusion coefficient (a matrix).

• hurst:: the Hurst parameter of the gaussian noise. If h=0.5, the process is Wiener otherwise it is fractional Brownian motion with that precise value of the Hurst index. Can be set to NA for further specification.

• jump.coeff:: a vector of expressions for the jump component.

• measure:: Levy measure for jump variables.

• measure.type:: Type specification for Levy measures.

• state.variable: a vector of names identifying the names used to denote the state variable in the drift and diffusion specifications.

• parameter:: which is a short name for ``parameters'', is an object of class model.parameter-class. For more details see model.parameter-class documentation page.

• state.variable:: identifies the state variables in the

   expression.
  

• jump.variable:: identifies the variable for the jump coefficient.

• time.variable:: the time variable.

• noise.number:: denotes the number of sources of noise. Currently only for the Gaussian part.

• equation.number:: denotes the dimension of the stochastic differential equation.

• dimension:: the dimensions of the parameter given in the parameter slot.

• solve.variable:: identifies the variable with respect to which the stochastic differential equation has to be solved.

• xinit:: contains the initial value of the stochastic differential equation.

• J.flag:: wheather jump.coeff include jump.variable.

Author(s)

The YUIMA Project Team

Contacts: Lorenzo Mercuri lorenzo.mercuri@unimi.it