## 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.

**Download:** **PDF**

### 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

**Unique-IP document downloads:** 1419 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*