{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:12:33Z","timestamp":1775466753332,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stoch. Dyn."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding L\u00e9vy process in the [Formula: see text] and [Formula: see text] Skorohod topologies has been studied in recent work. Here, we show that certain sufficient conditions for [Formula: see text]-convergence are also necessary. <\/jats:p>","DOI":"10.1142\/s0219493721500246","type":"journal-article","created":{"date-parts":[[2020,9,5]],"date-time":"2020-09-05T05:45:00Z","timestamp":1599284700000},"page":"2150024","source":"Crossref","is-referenced-by-count":4,"title":["Necessary and sufficient condition for \u21332-convergence to a L\u00e9vy process for billiards with cusps at flat points"],"prefix":"10.1142","volume":"21","author":[{"given":"Paul","family":"Jung","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, KAIST, Daejeon, South Korea"}]},{"given":"Ian","family":"Melbourne","sequence":"additional","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK"}]},{"given":"Fran\u00e7oise","family":"P\u00e8ne","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Brest, Institut Universitaire de France, LMBA, UMR CNRS 6205, 29238 Brest cedex, France"}]},{"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Federal da Bahia, 40170-110 Salvador, Brazil"}]},{"given":"Hong-Kun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Massachusetts, Amherst, MA, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,9,4]]},"reference":[{"key":"S0219493721500246BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-011-1342-6"},{"key":"S0219493721500246BIB002","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/ab5148"},{"key":"S0219493721500246BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-018-0726-y"},{"key":"S0219493721500246BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-019-03501-9"},{"key":"S0219493721500246BIB005","doi-asserted-by":"publisher","DOI":"10.1214\/13-AIHP586"},{"key":"S0219493721500246BIB006","series-title":"Cambridge Studies in Advanced Mathematics","volume-title":"L\u00e9vy Processes and Infinitely Divisible Distributions","volume":"68","author":"Sato K.-I.","year":"1999"},{"key":"S0219493721500246BIB007","first-page":"289","volume":"1","author":"Skorohod A. V.","year":"1956","journal-title":"Teor. Veroyatnost. i Primenen."},{"key":"S0219493721500246BIB008","doi-asserted-by":"publisher","DOI":"10.1287\/moor.5.1.67"},{"key":"S0219493721500246BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/b97479"},{"key":"S0219493721500246BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/698\/13983"}],"container-title":["Stochastics and Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219493721500246","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T09:54:28Z","timestamp":1628589268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219493721500246"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,4]]},"references-count":10,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S0219493721500246"],"URL":"https:\/\/doi.org\/10.1142\/s0219493721500246","relation":{},"ISSN":["0219-4937","1793-6799"],"issn-type":[{"value":"0219-4937","type":"print"},{"value":"1793-6799","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,4]]}}}