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Invariant Measures for Path-Dependent Random Diffusions

Jianhai Bao, Jinghai Shao, Chenggui Yuan Orcid Logo

ArXiv: 1706.05638

Swansea University Author: Chenggui Yuan Orcid Logo

Abstract

In this paper, we investigate the existence and uniqueness of invariant measure of stochastic functional differential equations with Markovian switching. Under an average condition, we prove that there is a unique measure for the exact solutions and the corresponding Euler numerical solutions. Moreo...

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Published in: ArXiv: 1706.05638
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URI: https://cronfa.swan.ac.uk/Record/cronfa36619
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first_indexed 2017-11-06T13:59:43Z
last_indexed 2023-04-14T02:46:16Z
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spelling v2 36619 2017-11-06 Invariant Measures for Path-Dependent Random Diffusions 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2017-11-06 SMA In this paper, we investigate the existence and uniqueness of invariant measure of stochastic functional differential equations with Markovian switching. Under an average condition, we prove that there is a unique measure for the exact solutions and the corresponding Euler numerical solutions. Moreover, the invariant measure of the Euler numerical solutions will converge to that of the exact solutions as the step size tends to zero. Journal Article ArXiv: 1706.05638 Invariant measure; Path-dependent random diffusion; Ergodicity; Wasserstein distance; Euler-Maruyama scheme 0 0 0 0001-01-01 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-05-22T14:04:52.2315211 2017-11-06T10:54:40.6529956 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 0036619-18062018105642.pdf 36619.pdf 2018-06-18T10:56:42.5800000 Output 344727 application/pdf Accepted Manuscript true 2018-06-18T00:00:00.0000000 true eng
title Invariant Measures for Path-Dependent Random Diffusions
spellingShingle Invariant Measures for Path-Dependent Random Diffusions
Chenggui Yuan
title_short Invariant Measures for Path-Dependent Random Diffusions
title_full Invariant Measures for Path-Dependent Random Diffusions
title_fullStr Invariant Measures for Path-Dependent Random Diffusions
title_full_unstemmed Invariant Measures for Path-Dependent Random Diffusions
title_sort Invariant 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 ArXiv: 1706.05638
institution Swansea University
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 paper, we investigate the existence and uniqueness of invariant measure of stochastic functional differential equations with Markovian switching. Under an average condition, we prove that there is a unique measure for the exact solutions and the corresponding Euler numerical solutions. Moreover, the invariant measure of the Euler numerical solutions will converge to that of the exact solutions as the step size tends to zero.
published_date 0001-01-01T14:04:50Z
_version_ 1766599625978937344
score 11.036706

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