{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:34:35Z","timestamp":1787322875123,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["254166"],"award-info":[{"award-number":["254166"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1517664"],"award-info":[{"award-number":["DMS 1517664"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>For a zero-sum stochastic game which does not satisfy the Isaacs condition, we provide a value function representation for an Isaacs-type equation whose Hamiltonian lies between the lower and upper Hamiltonians, as a convex combination of the two. For the general case (i.e., the convex combination is time and state dependent), our representation amounts to a random change of the rules of the game, to allow each player at any moment to see the other player's action or not, according to a coin toss with probabilities of heads and tails given by the convex combination appearing in the PDE. If the combination is state independent, then the rules can be set all in advance, in a deterministic way. This means that tossing the coin throughout the game, or tossing it repeatedly right at the beginning, leads to the same value. The representations are asymptotic over time discretizations. Space discretization is possible as well, leading to similar results.<\/jats:p>","DOI":"10.1137\/17m1128976","type":"journal-article","created":{"date-parts":[[2018,6,12]],"date-time":"2018-06-12T14:20:47Z","timestamp":1528813247000},"page":"2095-2119","source":"Crossref","is-referenced-by-count":5,"title":["Zero-Sum Stochastic Differential Games Without the Isaacs Condition: Random Rules of Priority and Intermediate Hamiltonians"],"prefix":"10.1137","volume":"56","author":[{"given":"Daniel","family":"Hern\u00e1ndez-Hern\u00e1ndez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihai","family":"S\u00eerbu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,6,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOP849"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1987210405571"},{"key":"atypb3","first-page":"271","volume":"4","author":"Barles G.","year":"1991","journal-title":"Asymptot. Anal."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2012-11336-X"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/12090352X"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2014-11860-0"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-008-9042-0"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1972-12929-X"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/0314006"},{"key":"atypb11","first-page":"341","volume":"5","author":"Fleming W. H.","year":"2011","journal-title":"Commun. Stoch. Anal."},{"key":"atypb12","first-page":"89","author":"Fleming W. H.","year":"2012","journal-title":"NJ"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1989.38.38015"},{"key":"atypb14","unstructured":"F. Gensbittel and C. Rainer,\n                      A Probabilistic Representation for the Value of Zero-Sum Differential Games with Incomplete Information on Both Sides\n                      , preprint,https:\/\/arxiv.org\/abs\/1602.06140, 2016."},{"key":"atypb15","unstructured":"F. Gensbittel and C. Rainer,\n                      A Two Player Zerosum Game Where Only One Player Observes a Brownian Motion\n                      , preprint,https:\/\/arxiv.org\/abs\/1610.02955, 2016."},{"key":"atypb16","unstructured":"R. Isaacs,\n                      Differential Games\n                      , John Wiley and Sons, Hoboken, NJ, 1965."},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"N. N. Krasovskii\u0306 and A. I. Subbotin,\n                      Game-Theoretical Control Problems\n                      , Springer Series in Soviet Mathematics, Springer-Verlag, New York, 1988.","DOI":"10.1007\/978-1-4612-3716-7"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-004-0818-6"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1017\/S0027763000002932"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/130929977"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/130929965"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/140968926"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"D. W. Stroock and S. R. S. Varadhan,\n                      Multidimensional Diffusion Processes\n                      , Classics in Mathematics, Springer-Verlag, Berlin, 2006, reprint of the 1997 edition.","DOI":"10.1007\/3-540-28999-2"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOP997"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1128976","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:30:52Z","timestamp":1787319052000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1128976"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1128976"],"URL":"https:\/\/doi.org\/10.1137\/17m1128976","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}