An algorithm for the computation of joint Hawkes moments with exponential kernel

10/25/2021
by   Nicolas Privault, et al.
0

The purpose of this paper is to present a recursive algorithm and its implementation in Maple and Mathematica for the computation of joint moments and cumulants of Hawkes processes with exponential kernels. Numerical results and computation times are also discussed. Obtaining closed form expressions can be computationally intensive, as joint fifth cumulant and moment formulas can be respectively expanded into up to 3,288 and 27,116 summands.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/13/2018

On moments of exponential functionals of additive processes

Let X = (X t) t>0 be a real-valued additive process, i.e., a process wit...
research
03/01/2018

Fast and accurate computation of orthogonal moments for texture analysis

In this work we propose a fast and stable algorithm for the computation ...
research
12/14/2020

Recursive computation of the Hawkes cumulants

We propose a recursive method for the computation of the cumulants of se...
research
07/02/2021

Moments of Subsets of General Equiangular Tight Frames

This note outlines the steps for proving that the moments of a randomly-...
research
06/28/2021

Exact simulation of extrinsic stress-release processes

We present a new and straightforward algorithm that simulates exact samp...
research
03/13/2018

On moments of integral exponential functionals of additive processes

Let X = (X t) t>0 be a real-valued additive process, i.e., a process wit...
research
06/26/2019

Correlators of Polynomial Processes

A process is polynomial if its extended generator maps any polynomial to...

Please sign up or login with your details

Forgot password? Click here to reset