{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:25:54Z","timestamp":1787322354166,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We study the large time behavior of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a backward SDE in finite horizon $T$ taken at initial time behaves like a linear term in $T$ shifted with the solution of the associated ergodic backward SDE taken at initial time. Moreover we give an explicit rate of convergence, which seems to be new to our best knowledge.<\/jats:p>","DOI":"10.1137\/140976091","type":"journal-article","created":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T15:44:44Z","timestamp":1422978284000},"page":"378-398","source":"Crossref","is-referenced-by-count":28,"title":["A Probabilistic Approach to Large Time Behavior of Mild Solutions of HJB Equations in Infinite Dimension"],"prefix":"10.1137","volume":"53","author":[{"given":"Ying","family":"Hu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre-Yves","family":"Madec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrien","family":"Richou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,2,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141000369344"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"G. Da Prato and J. Zabczyk,\n                      Stochastic Equations in Infinite Dimensions\n                      , Encyclopedia Math. Appl. 44, Cambridge University Press, Cambridge, UK, 1992.","DOI":"10.1017\/CBO9780511666223"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.11.009"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/07069849X"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1080\/104S1120290024856"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1029867132"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1080\/03605300500358087"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"D. Henry,\n                      Geometric Theory of Semilinear Parabolic Equations\n                      , Lecture Notes in Math. 840, Springer-Verlag, Berlin, 1981.","DOI":"10.1007\/BFb0089647"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/110832343"},{"key":"atypb10","first-page":"41","volume":"18","author":"McShane E. J.","year":"1967","journal-title":"Proc. Amer. Math. Soc."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s000300050029"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140976091","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:20:59Z","timestamp":1787318459000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140976091"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140976091"],"URL":"https:\/\/doi.org\/10.1137\/140976091","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}