{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:49:26Z","timestamp":1787320166787,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We study stochastic optimal control problems with a quadratic cost and linear state equation that involves stochastic coefficients and control dependent noise and, moreover, is perturbed by an affine term. Both the infinite horizon case and the ergodic case are treated. To this purpose we introduce a backward stochastic Riccati equation and a dual backward stochastic equation, both considered in the whole time line. Besides some stabilizability conditions we prove the existence of a solution for the two previous equations defined as limit of suitable finite horizon approximating problems. This allows us to perform the synthesis of the optimal control.<\/jats:p>","DOI":"10.1137\/070696234","type":"journal-article","created":{"date-parts":[[2009,5,8]],"date-time":"2009-05-08T12:31:25Z","timestamp":1241785885000},"page":"1600-1631","source":"Crossref","is-referenced-by-count":12,"title":["Infinite Horizon and Ergodic Optimal Quadratic Control for an Affine Equation with Stochastic Coefficients"],"prefix":"10.1137","volume":"48","author":[{"given":"Giuseppina","family":"Guatteri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Federica","family":"Masiero","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,5,7]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"A. Bensoussan,\n                      Lectures on stochastic control\n                      , in Proceedings of Nonlinear Filtering and Stochastic Control (Cortona, 1981), Lecture Notes in Math. 972, Springer, Berlin, 1982, pp. 1\u201362.","DOI":"10.1007\/BFb0064859"},{"key":"R2","first-page":"125","volume":"429","author":"Bensoussan A.","year":"1992","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0314028"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"J.M. Bismut,\n                      Contr\u00f4le des syst\u00e8mes lin\u00e9aires quadratiques: Applications de l'int\u00e9grale stochastique\n                      , in Proceedings of the S\u00e9minaire de Probabilit\u00e9s, XII, Lecture Notes in Math. 649, Springer, Berlin, 1978, pp. 180\u2013264.","DOI":"10.1007\/BFb0064606"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.06.006"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v13-514"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1997.3229"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01443614"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/1123091"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-007-9020-y"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"M. Kohlmann and S. Tang,\n                      New developments in backward stochastic Riccati equations and their applications\n                      , in Mathematical Finance (Konstanz, 2000), Trends Math., Birkh\u00e4user, Basel, 2001, pp. 194\u2013214.","DOI":"10.1007\/978-3-0348-8291-0_19"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(01)00133-8"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900378760"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S036301299834973X"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/0330018"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"S. Peng,\n                      Open problems on backward stochastic differential equations\n                      , in Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998), Kluwer Academic Publishers, Boston, 1999, pp. 265\u2013273.","DOI":"10.1007\/978-0-387-35359-3_32"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996313549"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901387550"},{"key":"R19","first-page":"1","volume":"8","author":"Tessitore G.","year":"1998","journal-title":"J. Math. Systems Estim. Control"},{"key":"R20","unstructured":"J. Yong and X. Z. Zhou,\n                      Stochastic Controls. Hamiltonian Systems and HJB Equations\n                      , Appl. Math. (N.Y.) 43, Springer-Verlag, New York, 1999."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070696234","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:55:30Z","timestamp":1787316930000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070696234"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070696234"],"URL":"https:\/\/doi.org\/10.1137\/070696234","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}