{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T00:29:39Z","timestamp":1787358579696,"version":"build-2736575974"},"reference-count":17,"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":[[2022,2]]},"abstract":"<jats:p>In this paper we study the limit of the value function for a two-scale, infinite-dimensional, stochastic controlled system with cylindrical noise and possibly degenerate diffusion. The limit is represented as the value function of a new reduced control problem (on a reduced state space). The presence of a cylindrical noise prevents representation of the limit by viscosity solutions of Hamilton--Jacobi--Bellman equations as in [\u015awi\u0229ch, ESAIM Control Optim. Calc. Var., to appear] while degeneracy of diffusion coefficients prevents representation as a classical backward stochastic differential equation as in [Guatteri and Tessitore, Appl. Math. Optim., 83 (2021), pp. 1025--1051]. We use a \u201cvanishing noise\u201d regularization technique.<\/jats:p>","DOI":"10.1137\/21m1408488","type":"journal-article","created":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T17:06:58Z","timestamp":1646068018000},"page":"575-596","source":"Crossref","is-referenced-by-count":4,"title":["Singular Limit of Two-Scale Stochastic Optimal Control Problems in Infinite Dimensions by Vanishing Noise Regularization"],"prefix":"10.1137","volume":"60","author":[{"given":"Giuseppina","family":"Guatteri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9893-3703","authenticated-orcid":true,"given":"Gianmario","family":"Tessitore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,2,28]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.11.009"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900366741"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-003-0266-5"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.05.027"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.3166\/ejc.17.30-45"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/090748147"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2018056"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1080\/104S1120290024856"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1029867132"},{"key":"atypb10","first-page":"1","volume":"23","author":"S. K.","year":"1987","journal-title":"Stochastics"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"F. G. Fabbri, F. Gozzi, and A.\u015awi\u0229ch,\n                      Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations\n                      , Probab. Theory Stoch. Model. 82, Springer, Cham, 2017,https:\/\/doi.org\/10.1007\/978-3-319-53067-3.","DOI":"10.1007\/978-3-319-53067-3"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-019-09577-y"},{"key":"atypb13","first-page":"200","author":"Kabanov Y. M.","year":"1991","journal-title":"Boston"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1080\/17442509108833713"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOP920"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"G. D. Prato and J. Zabczyk,\n                      Stochastic Equations in Infinite Dimensions\n                      , Encyclopedia Math. Appl. 44, Cambridge University Press, Cambridge, UK, 1992,https:\/\/doi.org\/10.1017\/CBO9780511666223.","DOI":"10.1017\/CBO9780511666223"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"G. D. Prato and J. Zabczyk,\n                      Ergodicity for Infinite-Dimensional Systems\n                      , London Math. Soc. Lecture Note Ser. 229, Cambridge University Press, Cambridge, UK, 1996.","DOI":"10.1017\/CBO9780511662829"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1408488","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:42:49Z","timestamp":1787316169000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1408488"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["10.1137\/21M1408488"],"URL":"https:\/\/doi.org\/10.1137\/21m1408488","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2]]}}}