# Compute the likelihood function of a hawkes process

### Description

Compute the likelihood function of a hawkes process for the given parameter and given the jump times vector (or list of vectors in the multivariate case), and until a time horizon.

### Usage

1 | ```
likelihoodHawkes(lambda0, alpha, beta, history)
``` |

### 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. |

`history` |
Jump times vector (or list of vectors in the multivariate case). |

### Value

Returns the opposite of the likelihood.

### 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
history<-simulateHawkes(lambda0,alpha,beta,3600)
l<-likelihoodHawkes(lambda0,alpha,beta,history[[1]])
#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)
history<-simulateHawkes(lambda0,alpha,beta,3600)
l<-likelihoodHawkes(lambda0,alpha,beta,history)
``` |

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