Exact simulation of extrinsic stress-release processes

TL;DR

This paper introduces an exact simulation algorithm for generalized stress-release processes, leveraging their joint interarrival times and martingale properties to ensure precise sample path generation and theoretical validation.

Contribution

The paper develops a new algorithm for exact simulation of stress-release processes, including derivation of their joint interarrival law and martingale generator, extending previous theoretical results.

Findings

Algorithm accurately simulates sample paths

Derived joint interarrival time distribution

Validated through theoretical moments

Abstract

We present a new and straightforward algorithm that simulates exact sample paths for a generalized stress-release process. The computation of the exact law of the joint interarrival times is detailed and used to derive this algorithm. Furthermore, the martingale generator of the process is derived and induces theoretical moments which generalize some results of Borovkov & Vere-Jones (2000) and are used to demonstrate the validity of our simulation algorithm.