# Mean of Hawkes process jumps.

### Description

The function returns the theoretical mean of the number of jumps of a Hawkes process on a time interval of length tau.

### Usage

1 |

### 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. |

`tau` |
Time interval length. |

### 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 containing the mean number of jumps of every process component.

### References

Jose Da Fonseca and Riadh Zaatour
Hawkes Process : Fast Calibration, Application to Trade Clustering and Diffusive Limit.
*Journal of Futures Markets*, Volume 34, Issue 6, pages 497-606, June 2014.

Jose Da Fonseca and Riadh Zaatour Clustering and Mean Reversion in Hawkes Microstructure Models.

### Examples

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