{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T14:42:29Z","timestamp":1701096149963},"reference-count":0,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[1978,2]]},"abstract":" Let X = {X(t), t \u2265 0} be a Markov storage process with compound Poisson input A = {A(t), t \u2265 0} and general release rule r(\u00b7). In a previous paper, a necessary and sufficient condition for the positive recurrence of X was obtained, and its stationary distribution was computed. Here we complete the recurrence classification of X, determining the conditions for null recurrence and transience. <\/jats:p> Closely related to X is a Markov process X0<\/jats:sup> = {X0<\/jats:sup>(t), t \u2265 0}. Its paths are absolutely continuous and increasing between downward jumps, the instantaneous rate of increase at time t being r(X0<\/jats:sup>(t)). The jumps are generated by A but are truncated as necessary to keep X nonnegative. It is shown that X0<\/jats:sup> is positive recurrent iff X is transient, null recurrent iff X is null recurrent, and transient iff X is positive recurrent. Furthermore, in the case where X0<\/jats:sup> is transient, the probability that X0<\/jats:sup> ever hits zero (viewed as a function of the initial state) has the same density as the stationary distribution of X. A similar duality between the two processes is found in the case where X0<\/jats:sup> is positive recurrent. <\/jats:p>","DOI":"10.1287\/moor.3.1.57","type":"journal-article","created":{"date-parts":[[2008,10,31]],"date-time":"2008-10-31T22:43:38Z","timestamp":1225493018000},"page":"57-66","source":"Crossref","is-referenced-by-count":42,"title":["The Recurrence Classification of Risk and Storage Processes"],"prefix":"10.1287","volume":"3","author":[{"given":"J. Michael","family":"Harrison","sequence":"first","affiliation":[{"name":"Graduate School of Business, Stanford University, Stanford, California 94305"}]},{"given":"Sidney I.","family":"Resnick","sequence":"additional","affiliation":[{"name":"Department of Statistics, Colorado State University, Fort Collins, Colorado 80523"}]}],"member":"109","container-title":["Mathematics of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubsonline.informs.org\/doi\/pdf\/10.1287\/moor.3.1.57","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T13:16:08Z","timestamp":1680441368000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubsonline.informs.org\/doi\/10.1287\/moor.3.1.57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1978,2]]}},"alternative-id":["10.1287\/moor.3.1.57"],"URL":"https:\/\/doi.org\/10.1287\/moor.3.1.57","relation":{},"ISSN":["0364-765X","1526-5471"],"issn-type":[{"value":"0364-765X","type":"print"},{"value":"1526-5471","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,2]]}}}