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Exact simulation of extrinsic stress-release processes

Part of: Stochastic processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 February 2022

Young Lee Open the ORCID record for Young Lee [Opens in a new window] ,
Patrick J. Laub ,
Thomas Taimre ,
Hongbiao Zhao  and
Jiancang Zhuang
Young Lee*
Affiliation:
Harvard University
Patrick J. Laub*
Affiliation:
University of New South Wales
Thomas Taimre*
Affiliation:
University of Queensland
Hongbiao Zhao*
Affiliation:
Shanghai University of Finance and Economics
Jiancang Zhuang*
Affiliation:
Institute of Statistical Mathematics
*
*Postal address: Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA. Email address:younglee@fas.harvard.edu
**Postal address: School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, Sydney, NSW 2052, Australia. Email address: p.laub@unsw.edu.au
***Postal address: School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia. Email address: t.taimre@uq.edu.au
****Postal address: Shanghai University of Finance and Economics, Yangpu District, Shanghai, 200433, China. Email address: h.zhao1@lse.ac.uk
*****Postal address: The Institute of Statistical Mathematics, 10-3 Midori-Cho, Tachikawa-Shi, Tokyo 190-8562, Japan. Email address: zhuangjc@ism.ac.jp
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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 inter-arrival 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 [3] and are used to demonstrate the validity of our simulation algorithm.

Keywords

Stress-release processinhibitory point process

MSC classification

Primary: 60G20: Generalized stochastic processes
Secondary: 60G55: Point processes 65C05: Monte Carlo methods
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 1 , March 2022 , pp. 105 - 117
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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