# simulateHawkes: Hawkes process simulation Function In hawkes: Hawkes process simulation and calibration toolkit

## Description

The function simulates a Hawkes process for the given parameter, and until a time horizon.

## Usage

 `1` ```simulateHawkes(lambda0, alpha, beta, horizon) ```

## Arguments

 `lambda0` Vector of initial intensity, a scalar in the monovariate case. `alpha` Matrix of excitation, a scalar in the monovariate case. Excitation values are all positive. `beta` Vector of betas, a scalar in the monovariate case. `horizon` Time horizon until which the simulation is to be conducted.

## Details

Notice that in the scalar case, one must have beta>alpha for the process to be stable, and in the multivariate case, the matrix (diag(beta)-alpha) must have eigen values with strictly positive real parts for the process to be stable.

## Value

Returns a vector of jump times in the monovariate case, and a list of such vectors for every component in the multivariate case.

## References

Y. Ogata. (1981) On Lewis simulation method for point processes. IEEE Transactions on Information Theory, 31

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```#One dimensional Hawkes process lambda0<-0.2 alpha<-0.5 beta<-0.7 horizon<-3600#one hour h<-simulateHawkes(lambda0,alpha,beta,horizon) #Multivariate Hawkes process lambda0<-c(0.2,0.2) alpha<-matrix(c(0.5,0,0,0.5),byrow=TRUE,nrow=2) beta<-c(0.7,0.7) horizon<-3600#one hour h<-simulateHawkes(lambda0,alpha,beta,horizon) ```

### Example output

```
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hawkes documentation built on May 31, 2017, 3:01 a.m.