# simbvh: Simulation of Bi-Variate Hawkes' Mutually Exciting Point... In SAPP: Statistical Analysis of Point Processes

 simbvh R Documentation

## Simulation of Bi-Variate Hawkes' Mutually Exciting Point Processes

### Description

Perform the simulation of bi-variate Hawkes' mutually exciting point processes. The response functions are parameterized by the Laguerre-type polynomials.

### Usage

``````simbvh(interval, axx = NULL, axy = NULL, axz = NULL, ayx = NULL,
ayy = NULL, ayz = NULL, c, d, c2, d2, ptxmax, ptymax)
``````

### Arguments

 `interval` length of time interval in which events take place. `axx` coefficients of Laguerre polynomial (lgp) of the transfer function (= response function) from the data events x to x (trf; x –> x). `axy` coefficients of lgp (trf; y –> x). `ayx` coefficients of lgp (trf; x –> y). `ayy` coefficients of lgp (trf; y –> y). `axz` coefficients of polynomial for x data. `ayz` coefficients of polynomial for y data. `c` exponential coefficient of lgp corresponding to xx. `d` exponential coefficient of lgp corresponding to xy. `c2` exponential coefficient of lgp corresponding to yx. `d2` exponential coefficient of lgp corresponding to yy. `ptxmax` an upper bound of trend polynomial corresponding to xz. `ptymax` an upper bound of trend polynomial corresponding to yz.

### Value

 `x` simulated data X. `y` simulated data Y.

### References

Ogata, Y., Katsura, K. and Zhuang, J. (2006) Computer Science Monographs, No.32, TIMSAC84: STATISTICAL ANALYSIS OF SERIES OF EVENTS (TIMSAC84-SASE) VERSION 2. The Institute of Statistical Mathematics.

Ogata, Y. (1981) On Lewis' simulation method for point processes. IEEE Information Theory, IT-27, pp.23-31.

### Examples

``````simbvh(interval = 20000,
axx = 0.01623,
axy = 0.007306,
axz = c(0.006187, -0.00000023),
ayz = c(0.0046786, -0.00000048, 0.2557e-10),
c = 0.4032, d = 0.0219, c2 = 1.0, d2 = 1.0,
ptxmax = 0.0062, ptymax = 0.08)
``````

SAPP documentation built on June 7, 2023, 5:45 p.m.