{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:48:31Z","timestamp":1740491311131,"version":"3.38.0"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p>In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding <jats:italic>q<\/jats:italic>-matrix <jats:italic>Q<\/jats:italic> is always regular and, thus, that the Feller minimal <jats:italic>Q<\/jats:italic>-process is honest, we obtain the exact value of the decay parameter \u03bb<jats:sub>\n                  <jats:italic>C<\/jats:italic>\n               <\/jats:sub>. We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always \u03bb<jats:sub>\n                  <jats:italic>C<\/jats:italic>\n               <\/jats:sub>-positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.<\/jats:p>","DOI":"10.1017\/s0021900200011554","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:50:01Z","timestamp":1459248601000},"page":"613-624","source":"Crossref","is-referenced-by-count":0,"title":["Uniqueness and Decay Properties of Markov Branching Processes with Disasters"],"prefix":"10.1017","volume":"51","author":[{"given":"Anyue","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai Wang","family":"Ng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanjun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S0021900200011554_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/1427118"},{"key":"S0021900200011554_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/1427670"},{"key":"S0021900200011554_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/1427037"},{"key":"S0021900200011554_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/1428100"},{"key":"S0021900200011554_ref15","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOP623"},{"key":"S0021900200011554_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02479830"},{"key":"S0021900200011554_ref14","first-page":"337","volume":"13","year":"1963","journal-title":"Proc. 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