{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T17:56:06Z","timestamp":1718733366748},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,7]]},"abstract":"<jats:p> Let \u03bc := (\u03bc<jats:sub>t<\/jats:sub>)<jats:sub>t &gt; 0<\/jats:sub> be a convolution semigroup on \u211d<jats:sup>d<\/jats:sup> endowed with its Lebesgue measure \u03bb. Let \u2133(\u03bc) be the set of all positive Borel measures \u03c9 on \u211d<jats:sup>d<\/jats:sup> for which \u03bc<jats:sub>t<\/jats:sub> * \u03c9 \u226a \u03bb, for each t &gt; 0. Let EX(\u03bc) be the set of all exit laws of \u03bc, i.e.the set of Borel functions \u03c6 :]0, \u221e[\u00d7 \u211d<jats:sup>d<\/jats:sup> \u21a6 [0, \u221e] which verifies the functional equation (by putting \u03c6<jats:sub>t<\/jats:sub> := \u03c6(t, .)) [Formula: see text] Under some \u03bb-regularity assumptions, it is proved in this paper that EX(\u03bc) can be identified with \u2133(\u03bc). <\/jats:p><jats:p> Moreover, let \u03bc<jats:sup>\u03b2<\/jats:sup> be the convolution semigroup obtained by subordination of \u03bc by a subordinator \u03b2 (i.e. [Formula: see text] where \u03b2 is a convolution semigroup on [0,\u221e[). It is also proved in this paper that, an exit law \u03c8 of \u03bc<jats:sup>\u03b2<\/jats:sup> is subordinated to some exit law of \u03bc, if and only if \u03c9 belongs to \u2133(\u03bc) where \u03c9 \u2208 \u2133(\u03bc<jats:sup>\u03b2<\/jats:sup>) is the associated measure to \u03c8 by the preceding identification. <\/jats:p>","DOI":"10.1142\/s0218127403007758","type":"journal-article","created":{"date-parts":[[2003,8,28]],"date-time":"2003-08-28T05:49:31Z","timestamp":1062049771000},"page":"1917-1922","source":"Crossref","is-referenced-by-count":1,"title":["On Subordination of Convolution Semigroups"],"prefix":"10.1142","volume":"13","author":[{"given":"Sonia Ben","family":"Othman","sequence":"first","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia"}]},{"given":"Slim","family":"Bouaziz","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia"}]},{"given":"Mohamed","family":"Hmissi","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences de Tunis, TN-1060 Tunis, Tunisia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66128-0"},{"key":"rf2","volume-title":"Probabilit\u00e9s et Potentiel","author":"Dellacherie C.","year":"1980"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01457159"},{"key":"rf4","first-page":"287","volume":"58","author":"Fitzsimmons P. J.","journal-title":"J. Func. Anal."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02567086"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF03025742"},{"key":"rf7","first-page":"63","volume":"196","author":"Hmissi M.","journal-title":"Rocznik Naukowo-Dydaktyczny WSP w Krakowie Prace Mat. XV"},{"key":"rf8","first-page":"221","volume":"339","author":"Hmissi M.","journal-title":"Grazer Math. Berichte"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007758","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:17:06Z","timestamp":1565122626000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007758"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7]]},"references-count":9,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,7]]}},"alternative-id":["10.1142\/S0218127403007758"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007758","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7]]}}}