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First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise / Jiao Song; Jiang-lun Wu; Hark Huang

Communications on Pure & Applied Analysis, Volume: 19, Issue: 8, Pages: 4127 - 4142

Swansea University Authors: Jiao, Song, Jiang-lun, Wu, Hark, Huang

  • Accepted Manuscript under embargo until: 29th May 2021

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DOI (Published version): 10.3934/cpaa.2020184

Abstract

The aim of this paper is twofold. Firstly, we derive an explicit expression of the (theoretical) solutions of stochastic differential equa- tions with affine coefficients driven by α-stable white noise. This is done by means of Itˆo formula. Secondly, we develop a detection al- gorithm for the first...

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Published in: Communications on Pure & Applied Analysis
ISSN: 1553-5258 1553-5258
Published: American Institute of Mathematical Sciences American Institute of Mathematical Sciences (AIMS) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53745
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Abstract: The aim of this paper is twofold. Firstly, we derive an explicit expression of the (theoretical) solutions of stochastic differential equa- tions with affine coefficients driven by α-stable white noise. This is done by means of Itˆo formula. Secondly, we develop a detection al- gorithm for the first jump time in simulation of sampling trajectories which are described by the solutions. The algorithm is carried out through a multivariate Lagrange interpolation approach. To this end, we utilise a computer simulation algorithm in MATLAB to visualise the sampling trajectories of the jump-diffusions for two combinations of parameters arising in the modelling structure of stochastic differ- ential equations with affine coefficients.
Issue: 8
Start Page: 4127
End Page: 4142