{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:37:27Z","timestamp":1759639047683},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2013,5,17]],"date-time":"2013-05-17T00:00:00Z","timestamp":1368748800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p>We examine a construction due to Fouch\u00e9 in which a Brownian motion is constructed from an algorithmically random infinite binary sequence. We show that although the construction is provably not computable in the sense of computable analysis, a lower bound for the rate of convergence is computable in any upper bound for the compressibilty of the sequence, making the construction layerwise computable.<\/jats:p>","DOI":"10.1017\/s0960129513000157","type":"journal-article","created":{"date-parts":[[2013,5,17]],"date-time":"2013-05-17T11:50:05Z","timestamp":1368791405000},"page":"1257-1265","source":"Crossref","is-referenced-by-count":3,"title":["On the computability of a construction of Brownian motion"],"prefix":"10.1017","volume":"23","author":[{"given":"GEORGE","family":"DAVIE","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"WILLEM L.","family":"FOUCH\u00c9","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2013,5,17]]},"reference":[{"key":"S0960129513000157_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(64)90223-2"},{"key":"S0960129513000157_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(66)80018-9"},{"key":"S0960129513000157_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-49820-1"},{"key":"S0960129513000157_ref22","first-page":"206","article-title":"Laws of information conservation (non-growth) and aspects of the foundation of probability theory.","volume":"10","author":"Levin","year":"1974","journal-title":"Problems of Information Transmission"},{"key":"S0960129513000157_ref20","first-page":"1","article-title":"Three approaches to the quantitative definition of information.","volume":"1","author":"Kolmogorov","year":"1965","journal-title":"Problems of Information Transmission"},{"key":"S0960129513000157_ref19","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2011-10741-X"},{"key":"S0960129513000157_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.09.045"},{"key":"S0960129513000157_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-21875-0_13"},{"key":"S0960129513000157_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(64)90131-7"},{"key":"S0960129513000157_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03073-4_27"},{"key":"S0960129513000157_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.03.054"},{"key":"S0960129513000157_ref12","unstructured":"Fouch\u00e9 W. L. (2013) Kolmogorov complexity and the geometry of Brownian motion (in preparation)."},{"key":"S0960129513000157_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03073-4_22"},{"key":"S0960129513000157_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2007.12.010"},{"key":"S0960129513000157_ref9","doi-asserted-by":"publisher","DOI":"10.1006\/aima.2000.1945"},{"key":"S0960129513000157_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68441-3"},{"key":"S0960129513000157_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04978-5"},{"key":"S0960129513000157_ref1","volume-title":"Individual random signals: an approach based on complexity","author":"Asarin","year":"1988"},{"key":"S0960129513000157_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00298-9"},{"key":"S0960129513000157_ref2","first-page":"21","article-title":"Use of the Kolmogorov complexity in analysing control system dynamics","volume":"47","author":"Asarin","year":"1986","journal-title":"Automation and Remote Control"},{"key":"S0960129513000157_ref21","volume-title":"Some theorems on the algorithmic approach to probability theory and information theory","author":"Levin","year":"1971"},{"key":"S0960129513000157_ref25","volume-title":"Computability and randomness","author":"Nies","year":"2008"},{"key":"S0960129513000157_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72734-7_22"},{"key":"S0960129513000157_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2008.12.009"},{"key":"S0960129513000157_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1015345756"},{"key":"S0960129513000157_ref4","doi-asserted-by":"publisher","DOI":"10.1145\/321892.321894"},{"key":"S0960129513000157_ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56999-9"},{"key":"S0960129513000157_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608858"},{"key":"S0960129513000157_ref8","doi-asserted-by":"publisher","DOI":"10.2307\/2586546"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129513000157","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T02:26:55Z","timestamp":1555986415000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129513000157\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,17]]},"references-count":29,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["S0960129513000157"],"URL":"https:\/\/doi.org\/10.1017\/s0960129513000157","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,17]]}}}