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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, Fangzhou Huang Orcid Logo

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

Swansea University Authors: Jiao Song, Jiang-lun Wu, Fangzhou Huang Orcid Logo

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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...

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Published in: Communications on Pure and Applied Analysis
ISSN: 1534-0392 1553-5258
Published: American Institute of Mathematical Sciences (AIMS) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53745
first_indexed 2020-06-24T13:07:41Z
last_indexed 2025-04-08T03:56:05Z
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spelling 2025-04-07T16:05:26.9305854 v2 53745 2020-03-05 First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise 074d2646201b4fdec08e10c300c68bd1 Jiao Song Jiao Song true false dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 056c3ea10b44f9eb5b15e965119478de 0000-0002-3789-8593 Fangzhou Huang Fangzhou Huang true false 2020-03-05 MACS 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. Journal Article Communications on Pure and Applied Analysis 19 8 4127 4142 American Institute of Mathematical Sciences (AIMS) 1534-0392 1553-5258 Stochastic differential equations, affine coefficients, α-stable processes, simulation, multivariate Lagrange interpolation 29 5 2020 2020-05-29 10.3934/cpaa.2020184 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Not Required 2025-04-07T16:05:26.9305854 2020-03-05T18:35:56.7889218 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jiao Song 1 Jiang-lun Wu 2 Fangzhou Huang 0000-0002-3789-8593 3 53745__16780__dc69f05066614c50a23a53fed6ce40bf.pdf affine.pdf 2020-03-05T18:41:29.7169375 Output 1161885 application/pdf Accepted Manuscript true 2021-05-29T00:00:00.0000000 true eng
title First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
spellingShingle First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
Jiao Song
Jiang-lun Wu
Fangzhou Huang
title_short First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
title_full First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
title_fullStr First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
title_full_unstemmed First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
title_sort First jump time in simulation of sampling trajectories of affine jump-diffusions driven by α-stable white noise
author_id_str_mv 074d2646201b4fdec08e10c300c68bd1
dbd67e30d59b0f32592b15b5705af885
056c3ea10b44f9eb5b15e965119478de
author_id_fullname_str_mv 074d2646201b4fdec08e10c300c68bd1_***_Jiao Song
dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
056c3ea10b44f9eb5b15e965119478de_***_Fangzhou Huang
author Jiao Song
Jiang-lun Wu
Fangzhou Huang
author2 Jiao Song
Jiang-lun Wu
Fangzhou Huang
format Journal article
container_title Communications on Pure and Applied Analysis
container_volume 19
container_issue 8
container_start_page 4127
publishDate 2020
institution Swansea University
issn 1534-0392
1553-5258
doi_str_mv 10.3934/cpaa.2020184
publisher American Institute of Mathematical Sciences (AIMS)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2020-05-29T04:46:30Z
_version_ 1856984045881131008
score 11.096295

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