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An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise

Guangjun Shen, Wentao Xu, Jiang-lun Wu

Acta Mathematica Scientia, Volume: 42, Issue: 2, Pages: 540 - 550

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1007/s10473-022-0208-7

Abstract

In this paper, we aim to derive an averaging principle for stochastic differential equations driven by time-changed L ́evy noise with variable delays. Under certain assump- tions, we show that the solutions of stochastic differential equations with time-changed L ́evy noise can be approximated by so...

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Published in: Acta Mathematica Scientia
ISSN: 0252-9602 1572-9087
Published: Springer Nature Switzerland AG. Springer Science and Business Media LLC 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa59180
first_indexed 2022-01-14T16:02:59Z
last_indexed 2025-01-09T20:07:34Z
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spelling 2025-01-02T11:23:14.1213466 v2 59180 2022-01-14 An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2022-01-14 In this paper, we aim to derive an averaging principle for stochastic differential equations driven by time-changed L ́evy noise with variable delays. Under certain assump- tions, we show that the solutions of stochastic differential equations with time-changed L ́evy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability, respectively. The convergence order is also estimated in terms of noise intensity. Finally, an example with numerical simulation is given to illustrate the theoretical result. Journal Article Acta Mathematica Scientia 42 2 540 550 Springer Science and Business Media LLC Springer Nature Switzerland AG. 0252-9602 1572-9087 Averaging principle; stochastic differential equation; time-changed Levy noise; variable delays. 1 3 2022 2022-03-01 10.1007/s10473-022-0208-7 COLLEGE NANME COLLEGE CODE Swansea University 2025-01-02T11:23:14.1213466 2022-01-14T15:42:35.3682080 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guangjun Shen 1 Wentao Xu 2 Jiang-lun Wu 3 59180__22145__59e75eb9a59b458ebfb9ada14bc9964c.pdf ShenXuWu-accepted version.pdf 2022-01-14T16:02:18.0798211 Output 394825 application/pdf Accepted Manuscript true 2023-02-03T00:00:00.0000000 true eng
title An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
spellingShingle An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
Jiang-lun Wu
title_short An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
title_full An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
title_fullStr An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
title_full_unstemmed An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
title_sort An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Lévy Noise
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Guangjun Shen
Wentao Xu
Jiang-lun Wu
format Journal article
container_title Acta Mathematica Scientia
container_volume 42
container_issue 2
container_start_page 540
publishDate 2022
institution Swansea University
issn 0252-9602
1572-9087
doi_str_mv 10.1007/s10473-022-0208-7
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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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
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description In this paper, we aim to derive an averaging principle for stochastic differential equations driven by time-changed L ́evy noise with variable delays. Under certain assump- tions, we show that the solutions of stochastic differential equations with time-changed L ́evy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability, respectively. The convergence order is also estimated in terms of noise intensity. Finally, an example with numerical simulation is given to illustrate the theoretical result.
published_date 2022-03-01T20:09:05Z
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