{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:48:27Z","timestamp":1740491307861,"version":"3.38.0"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2013,3]]},"abstract":"We study the exact asymptotics for the distribution of the first time, \u03c4\n x<\/jats:italic>\n <\/jats:sub>, a L\u00e9vy process X<\/jats:italic>\n \n t<\/jats:italic>\n <\/jats:sub> crosses a fixed negative level -x<\/jats:italic>. We prove that \u2119{\u03c4\n x<\/jats:italic>\n <\/jats:sub> &gt;t<\/jats:italic>} ~V<\/jats:italic>(x<\/jats:italic>) \u2119{X<\/jats:italic>\n \n t<\/jats:italic>\n <\/jats:sub>\u22650}\/t<\/jats:italic> as t<\/jats:italic>\u2192\u221e for a certain function V<\/jats:italic>(x<\/jats:italic>). Using known results for the large deviations of random walks, we obtain asymptotics for \u2119{\u03c4\n x<\/jats:italic>\n <\/jats:sub>&gt;t<\/jats:italic>} explicitly in both light- and heavy-tailed cases.<\/jats:p>","DOI":"10.1017\/s0021900200013127","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:49:16Z","timestamp":1459248556000},"page":"64-84","source":"Crossref","is-referenced-by-count":2,"title":["Asymptotics for the First Passage Times of L\u00e9vy Processes and Random Walks"],"prefix":"10.1017","volume":"50","author":[{"given":"Denis","family":"Denisov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vsevolod","family":"Shneer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"volume-title":"L\u00e9vy Processes and Infinitely Divisible Distributions","year":"1999","key":"S0021900200013127_ref29"},{"key":"S0021900200013127_ref1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019104402024"},{"key":"S0021900200013127_ref27","first-page":"656","volume":"11","year":"1966","journal-title":"Theory Prob. 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