{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:44:00Z","timestamp":1759970640355,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T00:00:00Z","timestamp":1738022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Beijing Natural science Foundation","doi-asserted-by":"publisher","award":["1222004"],"award-info":[{"award-number":["1222004"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Teacher Research Capacity Promotion of Beijing Normal University Zhuhai","award":["1222004"],"award-info":[{"award-number":["1222004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we consider a class of stochastic differential equations driven by multiplicative \u03b1-stable (0&lt;\u03b1&lt;2) L\u00e9vy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a concrete sufficient condition for the coefficients is presented, which is different from the conditions for SDEs driven by Brownian motion or general squared-integrable martingales. Finally, some ergodic and mixing properties are obtained by using the Foster\u2013Lyapunov criteria.<\/jats:p>","DOI":"10.3390\/axioms14020098","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T08:57:48Z","timestamp":1738054668000},"page":"98","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ergodicity and Mixing Properties for SDEs with \u03b1-Stable L\u00e9vy Noises"],"prefix":"10.3390","volume":"14","author":[{"given":"Siyan","family":"Xu","sequence":"first","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7068-0310","authenticated-orcid":false,"given":"Huiyan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Faculty of Arts and Sciences, Beijing Normal University at Zhuhai, Zhuhai 519087, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s00440-004-0426-z","article-title":"Systems of equations driven by stable processes","volume":"134","author":"Bass","year":"2006","journal-title":"Probab. 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