Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes
Let X t , Z t t ≥ 0 be the regime-switching jump diffusion process with invariant measure μ . We aim to approximate μ using the Euler–Maruyama (EM) scheme with decreasing step sequence Γ = ( γ n ) n ∈ N . Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coeffi...
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| Veröffentlicht in: | Journal of theoretical probability 2024-06, Vol.37 (2), p.1597-1626 |
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| container_title | Journal of theoretical probability |
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| creator | Chen, Peng Jin, Xinghu Shen, Tian Su, Zhonggen |
| description | Let
X
t
,
Z
t
t
≥
0
be the regime-switching jump diffusion process with invariant measure
μ
. We aim to approximate
μ
using the Euler–Maruyama (EM) scheme with decreasing step sequence
Γ
=
(
γ
n
)
n
∈
N
. Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coefficients of the related stochastic differential equation (SDE), we show that the error between
μ
and the invariant measure associated with the EM scheme is bounded by
O
(
γ
n
)
. In particular, we derive a better convergence rate
O
(
γ
n
)
for the additive case and the continuous case. |
| doi_str_mv | 10.1007/s10959-023-01253-w |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3060790563</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3060790563</sourcerecordid><originalsourceid>FETCH-LOGICAL-c249t-b1a4941add6a9f5dd3ece7e6bb2cc2fabdf4d2c487ba9dba203a8dcbfcb25ac13</originalsourceid><addsrcrecordid>eNp9kLtOAzEQRS0EEiHwA1QrURvG9r5cRiG8FATiVdBYttcOG2Uf2LsK6fgH_pAvwbBIdFTTnHtn5iB0SOCYAGQnngBPOAbKMBCaMLzeQiOSZBRzymAbjSDnMeZ5DLtoz_slAHAOMELPT9KVUq0Mvu9MG836lXGf7x_X0vUbWclo0raueSsr2ZVN7aPGRndmUVYBX5edfinrRXTVV210Wlrb-8BEt67Rxnvj99GOlStvDn7nGD2ezR6mF3h-c345ncyxpjHvsCIy5jGRRZFKbpOiYEabzKRKUa2plaqwcUF1nGdK8kJJCkzmhVZWK5pITdgYHQ294dLX3vhOLJve1WGlYJBCxiFJWaDoQGnXeO-MFa0Lb7mNICC-HYrBoQgOxY9DsQ4hNoR8gOuFcX_V_6S-ABNxeSc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3060790563</pqid></control><display><type>article</type><title>Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes</title><source>SpringerLink Journals</source><creator>Chen, Peng ; Jin, Xinghu ; Shen, Tian ; Su, Zhonggen</creator><creatorcontrib>Chen, Peng ; Jin, Xinghu ; Shen, Tian ; Su, Zhonggen</creatorcontrib><description>Let
X
t
,
Z
t
t
≥
0
be the regime-switching jump diffusion process with invariant measure
μ
. We aim to approximate
μ
using the Euler–Maruyama (EM) scheme with decreasing step sequence
Γ
=
(
γ
n
)
n
∈
N
. Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coefficients of the related stochastic differential equation (SDE), we show that the error between
μ
and the invariant measure associated with the EM scheme is bounded by
O
(
γ
n
)
. In particular, we derive a better convergence rate
O
(
γ
n
)
for the additive case and the continuous case.</description><identifier>ISSN: 0894-9840</identifier><identifier>EISSN: 1572-9230</identifier><identifier>DOI: 10.1007/s10959-023-01253-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Differential equations ; Ellipticity ; Error analysis ; Invariants ; Mathematics ; Mathematics and Statistics ; Probability Theory and Stochastic Processes ; Statistics ; Switching</subject><ispartof>Journal of theoretical probability, 2024-06, Vol.37 (2), p.1597-1626</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-b1a4941add6a9f5dd3ece7e6bb2cc2fabdf4d2c487ba9dba203a8dcbfcb25ac13</citedby><cites>FETCH-LOGICAL-c249t-b1a4941add6a9f5dd3ece7e6bb2cc2fabdf4d2c487ba9dba203a8dcbfcb25ac13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10959-023-01253-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10959-023-01253-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Chen, Peng</creatorcontrib><creatorcontrib>Jin, Xinghu</creatorcontrib><creatorcontrib>Shen, Tian</creatorcontrib><creatorcontrib>Su, Zhonggen</creatorcontrib><title>Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes</title><title>Journal of theoretical probability</title><addtitle>J Theor Probab</addtitle><description>Let
X
t
,
Z
t
t
≥
0
be the regime-switching jump diffusion process with invariant measure
μ
. We aim to approximate
μ
using the Euler–Maruyama (EM) scheme with decreasing step sequence
Γ
=
(
γ
n
)
n
∈
N
. Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coefficients of the related stochastic differential equation (SDE), we show that the error between
μ
and the invariant measure associated with the EM scheme is bounded by
O
(
γ
n
)
. In particular, we derive a better convergence rate
O
(
γ
n
)
for the additive case and the continuous case.</description><subject>Differential equations</subject><subject>Ellipticity</subject><subject>Error analysis</subject><subject>Invariants</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Statistics</subject><subject>Switching</subject><issn>0894-9840</issn><issn>1572-9230</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kLtOAzEQRS0EEiHwA1QrURvG9r5cRiG8FATiVdBYttcOG2Uf2LsK6fgH_pAvwbBIdFTTnHtn5iB0SOCYAGQnngBPOAbKMBCaMLzeQiOSZBRzymAbjSDnMeZ5DLtoz_slAHAOMELPT9KVUq0Mvu9MG836lXGf7x_X0vUbWclo0raueSsr2ZVN7aPGRndmUVYBX5edfinrRXTVV210Wlrb-8BEt67Rxnvj99GOlStvDn7nGD2ezR6mF3h-c345ncyxpjHvsCIy5jGRRZFKbpOiYEabzKRKUa2plaqwcUF1nGdK8kJJCkzmhVZWK5pITdgYHQ294dLX3vhOLJve1WGlYJBCxiFJWaDoQGnXeO-MFa0Lb7mNICC-HYrBoQgOxY9DsQ4hNoR8gOuFcX_V_6S-ABNxeSc</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Chen, Peng</creator><creator>Jin, Xinghu</creator><creator>Shen, Tian</creator><creator>Su, Zhonggen</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240601</creationdate><title>Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes</title><author>Chen, Peng ; Jin, Xinghu ; Shen, Tian ; Su, Zhonggen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-b1a4941add6a9f5dd3ece7e6bb2cc2fabdf4d2c487ba9dba203a8dcbfcb25ac13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Differential equations</topic><topic>Ellipticity</topic><topic>Error analysis</topic><topic>Invariants</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Statistics</topic><topic>Switching</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Peng</creatorcontrib><creatorcontrib>Jin, Xinghu</creatorcontrib><creatorcontrib>Shen, Tian</creatorcontrib><creatorcontrib>Su, Zhonggen</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of theoretical probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Peng</au><au>Jin, Xinghu</au><au>Shen, Tian</au><au>Su, Zhonggen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes</atitle><jtitle>Journal of theoretical probability</jtitle><stitle>J Theor Probab</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>37</volume><issue>2</issue><spage>1597</spage><epage>1626</epage><pages>1597-1626</pages><issn>0894-9840</issn><eissn>1572-9230</eissn><abstract>Let
X
t
,
Z
t
t
≥
0
be the regime-switching jump diffusion process with invariant measure
μ
. We aim to approximate
μ
using the Euler–Maruyama (EM) scheme with decreasing step sequence
Γ
=
(
γ
n
)
n
∈
N
. Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coefficients of the related stochastic differential equation (SDE), we show that the error between
μ
and the invariant measure associated with the EM scheme is bounded by
O
(
γ
n
)
. In particular, we derive a better convergence rate
O
(
γ
n
)
for the additive case and the continuous case.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10959-023-01253-w</doi><tpages>30</tpages></addata></record> |
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| identifier | ISSN: 0894-9840 |
| ispartof | Journal of theoretical probability, 2024-06, Vol.37 (2), p.1597-1626 |
| issn | 0894-9840 1572-9230 |
| language | eng |
| recordid | cdi_proquest_journals_3060790563 |
| source | SpringerLink Journals |
| subjects | Differential equations Ellipticity Error analysis Invariants Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Statistics Switching |
| title | Variable-Step Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes |
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