{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T07:39:09Z","timestamp":1791445149116,"version":"4.3.3"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"A","license":[{"start":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T00:00:00Z","timestamp":1459296000000},"content-version":"unspecified","delay-in-days":485,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>We look at joint regular variation properties of MA(\u221e) processes of the form<jats:bold><jats:italic>X<\/jats:italic><\/jats:bold>= (<jats:italic>X<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>,<jats:italic>k<\/jats:italic>\u2208<jats:bold>Z<\/jats:bold>), where<jats:italic>X<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>= \u2211<jats:sub><jats:italic>j<\/jats:italic>=0<\/jats:sub><jats:sup>\u221e<\/jats:sup>\u03c8<jats:sub><jats:italic>j<\/jats:italic><\/jats:sub><jats:italic>Z<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic>-<jats:italic>j<\/jats:italic><\/jats:sub>and the sequence of random variables (<jats:italic>Z<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>,<jats:italic>i<\/jats:italic>\u2208<jats:bold>Z<\/jats:bold>) are independent and identically distributed with regularly varying tails. We use the setup of<jats:bold>M<\/jats:bold><jats:sub><jats:bold>O<\/jats:bold><\/jats:sub>-convergence and obtain hidden regular variation properties for<jats:bold><jats:italic>X<\/jats:italic><\/jats:bold>under summability conditions on the constant coefficients (\u03c8<jats:sub><jats:italic>j<\/jats:italic><\/jats:sub>:<jats:italic>j<\/jats:italic>\u2265 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.<\/jats:p>","DOI":"10.1239\/jap\/1417528480","type":"journal-article","created":{"date-parts":[[2014,12,2]],"date-time":"2014-12-02T14:01:26Z","timestamp":1417528886000},"page":"267-279","source":"Crossref","is-referenced-by-count":5,"title":["Hidden regular variation of moving average processes with heavy-tailed innovations"],"prefix":"10.1017","volume":"51","author":[{"given":"Sidney I.","family":"Resnick","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joyjit","family":"Roy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S002190020002132X_ref18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025148622954"},{"key":"S002190020002132X_ref12","doi-asserted-by":"publisher","DOI":"10.3150\/08-BEJ125"},{"key":"S002190020002132X_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2004.09.003"},{"key":"S002190020002132X_ref8","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993074"},{"key":"S002190020002132X_ref6","volume-title":"An Introduction to the Theory of Point Processes. 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