{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:34:05Z","timestamp":1787319245203,"version":"build-2736575974"},"reference-count":25,"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":[[2020,1]]},"abstract":"<jats:p>In this paper we study an Ergodic Markovian BSDE involving a forward process $X$ that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the driver allows us to avoid the typical quantitative conditions relating the dissipativity of the forward equation and the Lipschitz constant of the driver. Although the degeneracy of the noise has to be of a suitable type, we can give a stochastic representation of a large class of Ergodic HJB equations; moreover, our general results can be applied to achieve the synthesis of the optimal feedback law in relevant examples of ergodic control problems for SPDEs.<\/jats:p>","DOI":"10.1137\/19m1292552","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T11:48:25Z","timestamp":1595418505000},"page":"2050-2077","source":"Crossref","is-referenced-by-count":4,"title":["Ergodic BSDEs with Multiplicative and Degenerate Noise"],"prefix":"10.1137","volume":"58","author":[{"given":"Giuseppina","family":"Guatteri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianmario","family":"Tessitore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,7,22]]},"reference":[{"key":"atypb1","unstructured":"J. P. Aubin,\n                      Applied Functional Analysis\n                      , 2nd ed., John Wiley & Sons, New York, Chichester, UK, Brisbane, AU, 1979, translated from the French by C. Labrousse, with exercises by B. Cornet and J.M. Lasry."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/120885875"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2015.12.009"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2018056"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"G. da Prato and J. Zabczyk,\n                      Ergodicity for infinite-dimensional Systems\n                      , London Math. Soc. Lecture Note Ser. 229, Cambridge University Press, Cambridge, 1996.","DOI":"10.1017\/CBO9780511662829"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1024404508"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.11.009"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2003.09.002"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/104S1120290024856"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1029867132"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-004-0814-x"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6387"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1142\/S0219493718500508"},{"key":"atypb14","unstructured":"Y. Hu and F. Lemonnier,\n                      Ergodic BSDE with an Unbounded and Multiplicative Underlying Diffusion and Application to Large Time Behavior of Viscosity Solution of HJB Equation\n                      , preprint,https:\/\/arxiv.org\/abs\/1801.01284, 2018."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/140976091"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-007-6029-5"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOP920"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"I. Lasiecka and R. Triggiani,\n                      Differential and algebraic Riccati equations with application to boundary\/point control problems: continuous theory and approximation theory\n                      , in Lect. Notes Control Inf. 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R\u0103\u015fcanu,\n                      Stochastic Differential Equations, Backward SDEs, Partial Differential Equations\n                      , in Stochastic Modelling and Applied Probability 69, Springer, Cham, 2014,https:\/\/doi.org\/10.1007\/978-3-319-05714-9.","DOI":"10.1007\/978-3-319-05714-9"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2009.03.005"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1080\/10451120410001696270"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1292552","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:46:56Z","timestamp":1787316416000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1292552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1292552"],"URL":"https:\/\/doi.org\/10.1137\/19m1292552","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}