{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T14:00:14Z","timestamp":1790517614110,"version":"4.1.0"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T00:00:00Z","timestamp":1469491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We define an isotropic L\u00e9vy-driven continuous auto-regressive moving average CARMA(p, q) random field on Rn as the integral of a radial CARMA kernel with respect to a L\u00e9vy sheet. Such fields constitute a parametric family characterized by an auto-regressive polynomial a and a moving average polynomial b having zeros in both the left and the right complex half-planes. They extend the well-balanced Ornstein\u2013Uhlenbeck process of Schnurr and Woerner to a well-balanced CARMA process in one dimension (with a much richer class of autocovariance functions) and to an isotropic CARMA random field on Rn for n &amp;gt; 1. We derive second-order properties of these random fields and extend the results to a larger class of anisotropic CARMA random fields. If the driving L\u00e9vy sheet is compound Poisson it is trivial to simulate the corresponding random field on any bounded subset of Rn. A method for joint estimation of the CARMA kernel parameters and knot locations is proposed for compound-Poisson-driven fields and is illustrated by applications to simulated data and Tokyo land price data.<\/jats:p>","DOI":"10.1111\/rssb.12197","type":"journal-article","created":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T12:10:32Z","timestamp":1469535032000},"page":"833-857","source":"Crossref","is-referenced-by-count":19,"title":["Continuous Auto-Regressive Moving Average Random Fields on Rn"],"prefix":"10.1093","volume":"79","author":[{"given":"Peter J.","family":"Brockwell","sequence":"first","affiliation":[{"name":"Colorado State University , Fort Collins , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yasumasa","family":"Matsuda","sequence":"additional","affiliation":[{"name":"Tohoku University , Sendai , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,7,26]]},"reference":[{"key":"2023021709315932700_rssb12197-cit-0001","volume-title":"Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz","year":"2012"},{"key":"2023021709315932700_rssb12197-cit-0002","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1007\/s10463-014-0468-7","article-title":"Recent results in the theory and applications of CARMA processes","volume":"66","author":"Brockwell","year":"2014","journal-title":"Ann. 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