## Exponential Hawkes Processes

**Authors:** Stephen Crowley

The Hawkes process having a kernel in the form of a linear combination of exponential functions ν(t)=sum_(j=1)^Pα_j*e^(-β_j*t) has a nice recursive structure that lends itself to tractable likelihood expressions. When P=1 the kernel is ν(t)=α e^(-β t) and the inverse of the compensator can be expressed in closed-form as a linear combination of exponential functions and the LambertW function having arguments which can be expressed as recursive functions of the jump times.

**Comments:** 12 Pages.

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### Submission history

[v1] 2012-11-16 15:47:51

[v2] 2012-11-19 18:25:11

[v3] 2012-11-22 14:48:59

[v4] 2012-11-29 12:25:23

[v5] 2012-12-12 10:24:21

[v6] 2012-12-31 16:05:15

[v7] 2013-01-12 16:33:02

[v8] 2013-01-30 12:59:09

[v9] 2015-11-20 17:57:17

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