{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T08:50:39Z","timestamp":1691657439369},"reference-count":49,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T00:00:00Z","timestamp":1661817600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2023,3]]},"abstract":"Abstract<\/jats:title>We analyse an additive-increase and multiplicative-decrease (also known as growth\u2013collapse) process that grows linearly in time and that, at Poisson epochs, experiences downward jumps that are (deterministically) proportional to its present position. For this process, and also for its reflected versions, we consider one- and two-sided exit problems that concern the identification of the laws of exit times from fixed intervals and half-lines. All proofs are based on a unified first-step analysis approach at the first jump epoch, which allows us to give explicit, yet involved, formulas for their Laplace transforms. All eight Laplace transforms can be described in terms of two so-called scale functions<\/jats:italic> associated with the upward one-sided exit time and with the upward two-sided exit time. All other Laplace transforms can be obtained from the above scale functions by taking limits, derivatives, integrals, and combinations of these.<\/jats:p>","DOI":"10.1017\/jpr.2022.27","type":"journal-article","created":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T11:32:28Z","timestamp":1661859148000},"page":"85-105","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Unified approach for solving exit problems for additive-increase and multiplicative-decrease processes"],"prefix":"10.1017","volume":"60","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-1331-9697","authenticated-orcid":false,"given":"Remco","family":"van der Hofstad","sequence":"first","affiliation":[]},{"given":"Stella","family":"Kapodistria","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-9257-1115","authenticated-orcid":false,"given":"Zbigniew","family":"Palmowski","sequence":"additional","affiliation":[]},{"given":"Seva","family":"Shneer","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,8,30]]},"reference":[{"key":"S0021900222000274_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-88264-7"},{"key":"S0021900222000274_ref25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511526251"},{"key":"S0021900222000274_ref6","doi-asserted-by":"publisher","DOI":"10.3390\/risks7040117"},{"key":"S0021900222000274_ref24","first-page":"80","article-title":"The first passage problem for generalized Ornstein\u2013Uhlenbeck processes with nonpositive jumps","author":"Hadjiev","year":"1985","journal-title":"S\u00e9minaire de Probabilit\u00e9s XIX"},{"key":"S0021900222000274_ref12","volume-title":"Probability","author":"Breiman","year":"1968"},{"key":"S0021900222000274_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/1969842"},{"key":"S0021900222000274_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/1426397"},{"key":"S0021900222000274_ref23","doi-asserted-by":"publisher","DOI":"10.2307\/1969621"},{"key":"S0021900222000274_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-31449-3_3"},{"key":"S0021900222000274_ref37","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200007889"},{"key":"S0021900222000274_ref41","first-page":"130","article-title":"The martingale approach in problems on the time of the first crossing of nonlinear boundaries","volume":"158","author":"Novikov","year":"1981","journal-title":"Trudy Mat. Inst. Steklov."},{"key":"S0021900222000274_ref42","first-page":"146","article-title":"Two-sided exit problem for a spectrally negative","volume":"12","author":"Patie","year":"2007","journal-title":"Electron. Commun. Prob."},{"key":"S0021900222000274_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-77913-1_5"},{"key":"S0021900222000274_ref44","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTP.0000020481.14371.37"},{"key":"S0021900222000274_ref45","doi-asserted-by":"publisher","DOI":"10.2307\/1427548"},{"key":"S0021900222000274_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2019.03.006"},{"key":"S0021900222000274_ref46","doi-asserted-by":"publisher","DOI":"10.1080\/03461238.1955.10414217"},{"key":"S0021900222000274_ref48","first-page":"329","article-title":"Uber eine zahlentheoretische Methode zur numerischen Integration und zur Behandlung von Integralgleichungen","author":"Tichy","year":"1984","journal-title":"Osterreichische Akademie der Wissenschaften Mathematisch-Naturwissenschaftliche Klasse Sitzungsberichte II 193"},{"key":"S0021900222000274_ref49","doi-asserted-by":"publisher","DOI":"10.1137\/1109090"},{"key":"S0021900222000274_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1034625257"},{"key":"S0021900222000274_ref5","doi-asserted-by":"publisher","DOI":"10.3390\/risks7010018"},{"key":"S0021900222000274_ref11","volume-title":"Markov Processes and Potential Theory","author":"Blumenthal","year":"1968"},{"key":"S0021900222000274_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.05.016"},{"key":"S0021900222000274_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2017.20"},{"key":"S0021900222000274_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2017.10.018"},{"key":"S0021900222000274_ref47","doi-asserted-by":"publisher","DOI":"10.2307\/3211975"},{"key":"S0021900222000274_ref15","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728918"},{"key":"S0021900222000274_ref27","volume-title":"Diffusion Processes and their Sample Paths","author":"Ito","year":"1965"},{"key":"S0021900222000274_ref8","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/28.5.514"},{"key":"S0021900222000274_ref2","first-page":"573","article-title":"Evaluating growth measures in populations subject to binomial and geometric catastrophes","volume":"4","author":"Artalejo","year":"2006","journal-title":"Math. Biosci. Eng."},{"key":"S0021900222000274_ref39","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s11134-009-9145-6","article-title":"TCP and iso-stationary transformations","volume":"63","author":"L\u00f6pker","year":"2009","journal-title":"Queueing Systems"},{"key":"S0021900222000274_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-31449-3_2"},{"key":"S0021900222000274_ref40","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-015-0755-3"},{"key":"S0021900222000274_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1075828052"},{"key":"S0021900222000274_ref18","doi-asserted-by":"publisher","DOI":"10.2307\/1425831"},{"key":"S0021900222000274_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/1969644"},{"key":"S0021900222000274_ref38","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995770"},{"key":"S0021900222000274_ref43","doi-asserted-by":"publisher","DOI":"10.2307\/1427849"},{"key":"S0021900222000274_ref26","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1075828048"},{"key":"S0021900222000274_ref20","doi-asserted-by":"publisher","DOI":"10.1137\/1113053"},{"key":"S0021900222000274_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2016.98"},{"key":"S0021900222000274_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0515036100015257"},{"key":"S0021900222000274_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.01.005"},{"key":"S0021900222000274_ref33","volume-title":"Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications","author":"Kyprianou","year":"2006"},{"key":"S0021900222000274_ref3","doi-asserted-by":"publisher","DOI":"10.1142\/7431"},{"key":"S0021900222000274_ref13","volume-title":"The Single Server Queue","author":"Cohen","year":"1982"},{"key":"S0021900222000274_ref17","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1019160951"},{"key":"S0021900222000274_ref34","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007810528683"},{"key":"S0021900222000274_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s11134-009-9112-2"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900222000274","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T09:03:39Z","timestamp":1675933419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900222000274\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,30]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["S0021900222000274"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2022.27","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,30]]},"assertion":[{"value":"\u00a9 The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}