{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:06Z","timestamp":1777449126070,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2014,6,1]],"date-time":"2014-06-01T00:00:00Z","timestamp":1401580800000},"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":[[2014,6]]},"abstract":"<jats:p>\n                    This work develops asymptotic properties of randomly switching and time inhomogeneous dynamic systems under Brownian perturbation with a small diffusion. The switching process is modeled by a continuous-time Markov chain, which portraits discrete events that cannot be modeled by a diffusion process. In the model, there are two small parameters. One of them is \u03b5 associated with the generator of the continuous-time, inhomogeneous Markov chain, and the other is \u03b4=\u03b4\n                    <jats:sub>\u03b5<\/jats:sub>\n                    signifies the small intensity of the diffusion. Assume \u03b5\u21920 and \u03b4\n                    <jats:sub>\u03b5<\/jats:sub>\n                    \u21920 as \u03b5\u21920. This paper focuses on large deviations type of estimates for such Markovian switching systems with small diffusions. The ratio \u03b5\/\u03b4\n                    <jats:sub>\u03b5<\/jats:sub>\n                    can be a nonzero constant, or equal to 0, or \u221e. These three different cases yield three different outcomes. This paper analyzes the three cases and present the corresponding asymptotic properties.\n                  <\/jats:p>","DOI":"10.3233\/asy-131198","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:32:34Z","timestamp":1575055954000},"page":"123-145","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Large deviations for multi-scale Markovian switching systems with a small diffusion"],"prefix":"10.1177","volume":"87","author":[{"given":"Qi","family":"He","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California, Irvine, CA 92697, USA. E-mail: qhe@math.uci.edu"}]},{"given":"G.","family":"Yin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. E-mail: gyin@math.wayne.edu"}]}],"member":"179","published-online":{"date-parts":[[2014,6,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131198","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131198","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:06Z","timestamp":1777380006000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131198"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.3233\/ASY-131198"],"URL":"https:\/\/doi.org\/10.3233\/asy-131198","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}