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Invariant probability measures for path-dependent random diffusions

Jianhai Bao, Jinghai Shao, Chenggui Yuan Orcid Logo

Nonlinear Analysis, Volume: 228, Start page: 113201

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1016/j.na.2022.113201

Abstract

In this work, we are concerned with path-dependent random diffusions. Under certain ergodic condition, we show that the path-dependent random diffusion under consideration has a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also,...

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Published in: Nonlinear Analysis
ISSN: 0362-546X
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62231
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first_indexed 2023-01-03T08:50:36Z
last_indexed 2023-02-04T04:13:24Z
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spelling 2023-02-03T13:33:41.9984290 v2 62231 2023-01-03 Invariant probability measures for path-dependent random diffusions 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2023-01-03 SMA In this work, we are concerned with path-dependent random diffusions. Under certain ergodic condition, we show that the path-dependent random diffusion under consideration has a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also, we demonstrate that the time discretization of the path-dependent random diffusion involved admits a unique (numerical) invariant probability measure and preserves the corresponding ergodic property when the step size is sufficiently small. Moreover, we provide an estimate on the exponential functional of the discrete observation for a Markov chain, which may be interesting by itself. Journal Article Nonlinear Analysis 228 113201 Elsevier BV 0362-546X Invariant probability measure; Path-dependent random diffusion; Ergodicity; Wasserstein distance; Euler–Maruyama scheme 1 3 2023 2023-03-01 10.1016/j.na.2022.113201 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-02-03T13:33:41.9984290 2023-01-03T08:47:17.2776135 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jianhai Bao 1 Jinghai Shao 2 Chenggui Yuan 0000-0003-0486-5450 3 62231__26160__c364138c13064854ac33ba507f7066de.pdf 62231.pdf 2023-01-03T08:49:18.8548962 Output 874109 application/pdf Version of Record true This is an open access article under the CC BY license true eng http://creativecommons.org/licenses/by/4.0/
title Invariant probability measures for path-dependent random diffusions
spellingShingle Invariant probability measures for path-dependent random diffusions
Chenggui Yuan
title_short Invariant probability measures for path-dependent random diffusions
title_full Invariant probability measures for path-dependent random diffusions
title_fullStr Invariant probability measures for path-dependent random diffusions
title_full_unstemmed Invariant probability measures for path-dependent random diffusions
title_sort Invariant probability measures for path-dependent random diffusions
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Jianhai Bao
Jinghai Shao
Chenggui Yuan
format Journal article
container_title Nonlinear Analysis
container_volume 228
container_start_page 113201
publishDate 2023
institution Swansea University
issn 0362-546X
doi_str_mv 10.1016/j.na.2022.113201
publisher Elsevier BV
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 In this work, we are concerned with path-dependent random diffusions. Under certain ergodic condition, we show that the path-dependent random diffusion under consideration has a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also, we demonstrate that the time discretization of the path-dependent random diffusion involved admits a unique (numerical) invariant probability measure and preserves the corresponding ergodic property when the step size is sufficiently small. Moreover, we provide an estimate on the exponential functional of the discrete observation for a Markov chain, which may be interesting by itself.
published_date 2023-03-01T04:21:41Z
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score 11.016235

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