{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:47:43Z","timestamp":1740491263164,"version":"3.38.0"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2013,3]]},"abstract":"<jats:p>Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein\u2013Uhlenbeck or fractional Cox\u2013Ingersoll\u2013Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.<\/jats:p>","DOI":"10.1017\/s0021900200013188","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:49:16Z","timestamp":1459248556000},"page":"166-183","source":"Crossref","is-referenced-by-count":3,"title":["Conditional Distributions of Processes Related to Fractional Brownian Motion"],"prefix":"10.1017","volume":"50","author":[{"given":"Holger","family":"Fink","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claudia","family":"Kl\u00fcppelberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martina","family":"Z\u00e4hle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200013188_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/3318624"},{"volume-title":"Stable Non-Gaussian Random Processes","year":"1994","key":"S0021900200013188_ref20"},{"key":"S0021900200013188_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/08-AAP586"},{"key":"S0021900200013188_ref16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010432716012"},{"first-page":"417","volume-title":"Theory and Applications of Long-Range Dependence","year":"2003","key":"S0021900200013188_ref15"},{"key":"S0021900200013188_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2011.03.028"},{"key":"S0021900200013188_ref14","doi-asserted-by":"publisher","DOI":"10.2307\/2951677"},{"key":"S0021900200013188_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2005.06.014"},{"key":"S0021900200013188_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s10436-008-0110-x"},{"key":"S0021900200013188_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1060202833"},{"key":"S0021900200013188_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP461"},{"volume-title":"Credit Risk Modeling with Affine Processes","year":"2004","key":"S0021900200013188_ref6"},{"key":"S0021900200013188_ref11","doi-asserted-by":"publisher","DOI":"10.2307\/3215063"},{"volume-title":"Real Analysis and Probability","year":"2006","key":"S0021900200013188_ref5"},{"key":"S0021900200013188_ref10","doi-asserted-by":"publisher","DOI":"10.3150\/10-BEJ281"},{"key":"S0021900200013188_ref4","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1151525129"},{"key":"S0021900200013188_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.12.006"},{"key":"S0021900200013188_ref2","doi-asserted-by":"publisher","DOI":"10.1080\/19451120310001642613"},{"key":"S0021900200013188_ref1","doi-asserted-by":"publisher","DOI":"10.2307\/2077735"},{"key":"S0021900200013188_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s004400050171"},{"key":"S0021900200013188_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02401743"},{"key":"S0021900200013188_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s440-000-8016-7"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200013188","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,4,21]],"date-time":"2017-04-21T15:55:59Z","timestamp":1492790159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200013188\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3]]},"references-count":22,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["S0021900200013188"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200013188","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"type":"print","value":"0021-9002"},{"type":"electronic","value":"1475-6072"}],"subject":[],"published":{"date-parts":[[2013,3]]}}}