{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:40:37Z","timestamp":1682502037911},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>We derive multivariate moment generating functions for the conditional and stationary distributions of a discrete sample path of <jats:italic>n<\/jats:italic> observations of a square-root diffusion (CIR) process, <jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>). For any fixed vector of observation times <jats:italic>t<\/jats:italic>\n               <jats:sub>1<\/jats:sub>,\u2026,<jats:italic>t<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub>, we find the conditional joint distribution of (<jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>\n               <jats:sub>1<\/jats:sub>),\u2026,<jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub>)) is a multivariate noncentral chi-squared distribution and the stationary joint distribution is a Krishnamoorthy-Parthasarathy multivariate gamma distribution. Multivariate cumulants of the stationary distribution have a simple and computationally tractable expression. We also obtain the moment generating function for the increment <jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic> + \u03b4) - <jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>), and show that the increment is equivalent in distribution to a scaled difference of two independent draws from a gamma distribution.<\/jats:p>","DOI":"10.1017\/s002190020001189x","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:14Z","timestamp":1459263074000},"page":"930-942","source":"Crossref","is-referenced-by-count":0,"title":["Finite-Dimensional Distributions of a Square-Root Diffusion"],"prefix":"10.1017","volume":"51","author":[{"given":"Michael B.","family":"Gordy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S002190020001189X_ref9","doi-asserted-by":"publisher","DOI":"10.1137\/0117072"},{"key":"S002190020001189X_ref10","doi-asserted-by":"publisher","DOI":"10.1198\/073500102317351958"},{"key":"S002190020001189X_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/1969318"},{"key":"S002190020001189X_ref5","doi-asserted-by":"publisher","DOI":"10.2307\/1911242"},{"key":"S002190020001189X_ref4","volume-title":"Financial Modelling with Jump Processes","year":"2004"},{"key":"S002190020001189X_ref16","volume-title":"Linear Systems","volume":"1","year":"2008"},{"key":"S002190020001189X_ref3","volume-title":"Advanced Combinatorics: The Art of Finite and Infinite Expansions","year":"1974"},{"key":"S002190020001189X_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01720592"},{"key":"S002190020001189X_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1992.tb04011.x"},{"key":"S002190020001189X_ref14","first-page":"348","volume":"22","year":"1960","journal-title":"J. R. Statist. Soc. B"},{"key":"S002190020001189X_ref1","first-page":"401","volume-title":"Encyclopedia of Quantitative Finance","year":"2010"},{"key":"S002190020001189X_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729544"},{"key":"S002190020001189X_ref12","volume-title":"Models and Applications","volume":"1","year":"2000"},{"key":"S002190020001189X_ref11","volume-title":"Continuous Univariate Distributions","volume":"1","year":"1994"},{"key":"S002190020001189X_ref8","volume-title":"Matrix Analysis","year":"1985"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002190020001189X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:15:48Z","timestamp":1682500548000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002190020001189X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":15,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S002190020001189X"],"URL":"https:\/\/doi.org\/10.1017\/s002190020001189x","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}