The function returns the theoretical mean of the number of jumps of a Hawkes process on a time interval of length tau.
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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. |
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.
Returns a vector containing the mean number of jumps of every process component.
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.
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