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First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
Communications on Pure and Applied Analysis, Volume: 19, Issue: 8, Pages: 4127 - 4142
Swansea University Authors:
Jiao Song, Jiang-lun Wu, Fangzhou Huang
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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 equations with affine coefficients driven by α-stable white noise. This is done by means of Itô formula. Secondly, we develop a detection algorithm for the first jump...
| Published in: | Communications on Pure and Applied Analysis |
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| ISSN: | 1534-0392 1553-5258 |
| Published: |
American Institute of Mathematical Sciences (AIMS)
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa53745 |
| Abstract: |
The aim of this paper is twofold. Firstly, we derive an explicit expression of the (theoretical) solutions of stochastic differential equations with affine coefficients driven by α-stable white noise. This is done by means of Itô formula. Secondly, we develop a detection algorithm 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 differential equations with affine coefficients. |
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| Keywords: |
Stochastic differential equations, affine coefficients, α-stable processes, simulation, multivariate Lagrange interpolation |
| College: |
Faculty of Science and Engineering |
| Issue: |
8 |
| Start Page: |
4127 |
| End Page: |
4142 |