{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:06:17Z","timestamp":1787702777489,"version":"build-2784847793"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic filtering and statistics demonstrate the practical relevance of our result.<\/jats:p>","DOI":"10.1137\/140995982","type":"journal-article","created":{"date-parts":[[2015,9,2]],"date-time":"2015-09-02T10:31:35Z","timestamp":1441189895000},"page":"2762-2780","source":"Crossref","is-referenced-by-count":3,"title":["The Inverse Problem for Rough Controlled Differential Equations"],"prefix":"10.1137","volume":"53","author":[{"given":"I.","family":"Bailleul","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Diehl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,9,2]]},"reference":[{"key":"atypb1","unstructured":"I. Bailleul,\n                      A Flow-Based Approach to Rough Differential Equations\n                      , preprint, arXiv: 1404.0890, 2014."},{"key":"atypb2","first-page":"31","author":"Bailleul I.","year":"2015","journal-title":"Rev. Mat. Iberoamericana"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"A. M. Bloch,\n                      Nonholonomic Mechanics and Control\n                      , Interdiscip. Appl. Math. 24, Springer, 2003.","DOI":"10.1007\/b97376"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"U. Boscain, T. Chambrion, and G. Charlot,\n                      Nonisotropic $3$-Level Quantum Systems: Complete Solutions for Minimum Time and Minimum Energy\n                      , preprint, arXiv:quant-ph\/0409022, 2004.","DOI":"10.3934\/dcdsb.2005.5.957"},{"key":"atypb6","unstructured":"Y. Boutaib, L. Gyurko, T. Lyons, and D. Yang,\n                      Dimension-Free Euler Estimates of Rough Differential Equations\n                      , preprint, arXiv:1307.4708, 2013."},{"key":"atypb7","first-page":"1","author":"Brockett R. W.","year":"1993","journal-title":"Springer US"},{"key":"atypb8","unstructured":"M. Caruana, T. Le\u0301vy, and T. Lyons,\n                      Differential Equations Driven by Rough Paths\n                      , Lecture Notes in Math. 1908, Springer, Berlin, 2007."},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"J. M. C. Clark,\n                      The design of robust approximations to the stochastic differential equations of nonlinear filtering\n                      , in Communication Systems and Random Process Theory, NATO Advanced Study Inst. Ser. E Appl. Sci. 25, Sijthoff & Noordhoff, Alphen aan den Rijn, 1978, pp. 721-734.","DOI":"10.1007\/978-94-011-7577-7_41"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1214\/12-AAP896"},{"key":"atypb11","unstructured":"A. M. Davie,\n                      Differential equations driven by rough paths: An approach via discrete approximation\n                      , Appl. Math. Res. Express. AMRX, 2007, abm009."},{"key":"atypb12","first-page":"403","author":"M. H.","year":"2011","journal-title":"Oxford"},{"key":"atypb13","unstructured":"J. Diehl, P. Friz., and H. Mai,\n                      Pathwise Stability of Likelihood Estimators for Diffusions via Rough Paths\n                      , preprint, arXiv:1311.1061, 2013."},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"P. Friz and M. Hairer,\n                      A Course on Rough Paths\n                      , Springer, Cham, 2014.","DOI":"10.1007\/978-3-319-08332-2"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"P. K. Friz and N. B. Victoir,\n                      Multidimensional Stochastic Processes as Rough Paths: Theory and Applications\n                      , Cambridge Stud. Adv. Math. 120, Cambridge University Press, Cambridge, UK, 2010.","DOI":"10.1017\/CBO9780511845079"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2004.01.002"},{"key":"atypb17","unstructured":"L. Gyurko, T. Lyons, M. Kontkowski, and J. Field,\n                      Extracting Information from the Signature of a Financial Data Stream\n                      , preprint, arXiv:1307.7244, 2013."},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"M. Hirsch,\n                      Differential Topology\n                      , Springer, 1976.","DOI":"10.1007\/978-1-4684-9449-5"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(02)00176-X"},{"key":"atypb20","unstructured":"D. Levin, T. Lyons, and H. Ni,\n                      Learning from the Past, Predicting the Statistics for the Future, Learning an Evolving System\n                      , preprint, arXiv:1309.0260, 2013."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.4171\/rmi\/240"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"T. Lyons, M. Caruana, and T. Le\u0301vy,\n                      Differential equations driven by rough paths\n                      , Saint Flour Lecture Notes, Lecture Notes in Math. 1908, Springer, Berlin, 2007.","DOI":"10.1007\/978-3-540-71285-5"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"T. Lyons and Z. Qian,\n                      System Control and Rough Paths\n                      , Oxford University Press, Oxford, 2002.","DOI":"10.1093\/acprof:oso\/9780198506485.001.0001"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2003.1239"},{"key":"atypb25","unstructured":"T. Lyons and D. Yang,\n                      Rough Differential Equation in Banach Space Driven by Weak Geometric p-Rough Path\n                      , preprint, arXiv:1402.2900, 2014."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2014.34.1121"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(87)90091-7"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02401743"},{"key":"atypb29","unstructured":"E. Zeidler,\n                      Nonlinear Functional Analysis and Its Applications: Part 4: Applications to Mathematical Physics\n                      , Springer, 1997."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140995982","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:23:46Z","timestamp":1787318626000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140995982"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140995982"],"URL":"https:\/\/doi.org\/10.1137\/140995982","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}