{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T06:25:01Z","timestamp":1788330301617,"version":"build-2803163510"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>This paper is concerned with the null controllability for general forward and backward linear stochastic parabolic equations. To develop the duality argument, we establish observability estimates for linear backward and forward stochastic parabolic equations with general coefficients, by means of a global Carleman estimate. Our Carleman inequality (Theorem 6.1) and observability estimate (Theorem 2.3) for backward stochastic parabolic equations are new in their forms. By adding a control variable to act on the white noise, we give a partial solution to the null controllability of forward stochastic heat equations, which was regarded as a challenging topic (see pages 99 and 108\u2013110 in [Barbu, R\u0103scanu, and Tessitore, Appl. Math. Optim., 47 (2003), pp. 97\u2013120]).<\/jats:p>","DOI":"10.1137\/050641508","type":"journal-article","created":{"date-parts":[[2009,6,25]],"date-time":"2009-06-25T18:04:45Z","timestamp":1245953085000},"page":"2191-2216","source":"Crossref","is-referenced-by-count":112,"title":["Null Controllability for Forward and Backward Stochastic Parabolic Equations"],"prefix":"10.1137","volume":"48","author":[{"given":"Shanjian","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,6,25]]},"reference":[{"key":"R1","first-page":"143","volume":"56","author":"Barbu V.","year":"2002","journal-title":"Sci. Math. 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Imanuvilov,\n                      Controllability of Evolution Equations\n                      , Lecture Notes Ser. 34, Research Institute of Mathematics, Seoul National University, Seoul, Korea, 1994."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1080\/07362999108809250"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1145476103"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01192260"},{"key":"R12","unstructured":"J. Ma and J. Yong,\n                      Forward-Backward Differential Equations and Their Applications\n                      , Lecture Notes in Math. 1702, Springer, Berlin, 1999."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.09.036"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1080\/07362999608809451"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025459624398"},{"key":"R16","doi-asserted-by":"crossref","first-page":"81","DOI":"10.57262\/die\/1356039060","volume":"21","author":"Zhang X.","year":"2008","journal-title":"Differential Integral Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0893-4983","issn-type":"print"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(92)90122-Y"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"E. Zuazua,\n                      Controllability and observability of partial differential equations: Some results and open problems\n                      , in Handbook of Differential Equations: Evolutionary Equations, Vol. 3, Elsevier Science, Amsterdam, 2006, pp. 527\u2013621.","DOI":"10.1016\/S1874-5717(07)80010-7"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050641508","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:51:22Z","timestamp":1787316682000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050641508"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/050641508"],"URL":"https:\/\/doi.org\/10.1137\/050641508","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}