{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:50Z","timestamp":1777447910661,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2018,8,3]],"date-time":"2018-08-03T00:00:00Z","timestamp":1533254400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,8,3]]},"abstract":"<jats:p>In this paper, we consider recurrence of bounded solutions to semilinear stochastic integro-differential equations via uniformly exponentially stable resolvent operators family. Concretely, we first establish the existence and uniqueness of the [Formula: see text]-bounded solution to a semilinear stochastic integro-differential equations driven by L\u00e9vy processes, and then we show this kind of [Formula: see text]-bounded solution is almost automorphic in distribution or weighted pseudo almost automorphic in distribution under suitable conditions respectively.<\/jats:p>","DOI":"10.3233\/asy-181466","type":"journal-article","created":{"date-parts":[[2018,9,18]],"date-time":"2018-09-18T15:47:41Z","timestamp":1537285661000},"page":"27-52","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Recurrence of bounded solutions to a semilinear integro-differential equation perturbed by L\u00e9vy noise"],"prefix":"10.1177","volume":"109","author":[{"given":"Yong-Kui","family":"Chang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xidian University, Xi\u2019an, Shaanxi 710071, China. 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E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,8,3]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.07.013"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0252-9602(12)60211-2"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809781"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.12.020"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9476-9"},{"key":"ref006","unstructured":"Y.T.\u00a0Bian, Y.K.\u00a0Chang and J.J.\u00a0Nieto, Weighted asymptotic behavior of solutions to a semilinear integro-differential equation in Banach spaces, Electronic Journal of Differential Equations 2014 (2014), 91."},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1080\/17442508.2010.533375"},{"key":"ref008","unstructured":"Y.K.\u00a0Chang and R.\u00a0Ponce, Uniform exponential stability and its applications to bounded solutions of integro\u2013differential equations in Banach spaces, to appear in\n                      Journal of Integral Equations and Applications\n                      ."},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1080\/17442508.2016.1178748"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-009-0028-4"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2011.03.005"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.10.008"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.04.017"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-10-10377-3"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2015.02.036"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2015.02.071"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2013.11.011"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.02.018"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810947"},{"key":"ref020","doi-asserted-by":"crossref","unstructured":"G.M.\u00a0N\u2019Gu\u00e9r\u00e9kata, Almost Automorphic and Almost Periodic Functions in Abstract Space, Kluwer, New York, 2001.","DOI":"10.1007\/978-1-4757-4482-8"},{"key":"ref021","unstructured":"G.M.\u00a0N\u2019Gu\u00e9r\u00e9kata, Topics in Almost Automorphy, Springer, New York, 2005."},{"key":"ref022","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511721373"},{"key":"ref023","doi-asserted-by":"crossref","unstructured":"J.\u00a0Pr\u00fcss, Evolutionary Integral Equations and Applications, Birkh\u00e4user Verlag, 1993.","DOI":"10.1007\/978-3-0348-8570-6"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2009.11.004"},{"key":"ref025","doi-asserted-by":"publisher","DOI":"10.1063\/1.4739406"},{"key":"ref026","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2015.1090562"},{"key":"ref027","doi-asserted-by":"publisher","DOI":"10.1002\/mma.3108"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181466","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-181466","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181466","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:13Z","timestamp":1777379773000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-181466"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,3]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,8,3]]}},"alternative-id":["10.3233\/ASY-181466"],"URL":"https:\/\/doi.org\/10.3233\/asy-181466","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,3]]}}}