{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T01:44:10Z","timestamp":1787363050917,"version":"build-2736575974"},"reference-count":18,"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":[[2002,1]]},"abstract":"<jats:p>\n                    We consider a zero-sum game of optimal stopping in which each of the opponents has the right to stop a one-dimensional diffusion process. There are two types of costs. The first is accumulated continuously at the rate H(X\n                    <jats:sub>t<\/jats:sub>\n                    ), where X\n                    <jats:sub>t<\/jats:sub>\n                    is the current position of the process. The second is a cost associated with the stopping of the process. It is given by the function f\n                    <jats:sub>1<\/jats:sub>\n                    (x) for the first player and the function f\n                    <jats:sub>2<\/jats:sub>\n                    (x) for the second player, where x is the position of the process when the stopping option is exercised. We study the solution of the free boundary problem associated with this game via Dirichlet forms on the appropriate functional space. Integrating the value function of the game, we get a solution to another free boundary problem which yields the optimal return function for a singular stochastic control problem.\n                  <\/jats:p>","DOI":"10.1137\/s0363012901387136","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"682-699","source":"Crossref","is-referenced-by-count":10,"title":["Dynkin Games via Dirichlet Forms and Singular Control of One-Dimensional Diffusions"],"prefix":"10.1137","volume":"41","author":[{"given":"Masatoshi","family":"Fukushima","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Taksar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","volume-title":"Applications of variational inequalities in stochastic control","author":"Bensoussan Alain","year":"1982"},{"key":"R2","first-page":"16","volume":"185","author":"Dynkin E.","year":"1969","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"R3","volume-title":"Controlled Markov processes and viscosity solutions","author":"Fleming Wendell","year":"1993"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v4-55"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1515\/9783110889741"},{"key":"R6","first-page":"732","volume":"14","author":"Guse n\u2010Zade S.","year":"1969","journal-title":"Teor. Verojatnost. i Primenen."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.3.439"},{"key":"R8","volume-title":"Stochastic differential equations and diffusion processes","author":"Ikeda Nobuyuki","year":"1989"},{"key":"R9","unstructured":"K. Ito and H. P. McKean,\n                      Diffusion Processes and Their Sample Paths\n                      , Springer\u2010Verlag, Berlin, Heidelberg, New York, 1974."},{"key":"R10","unstructured":"I. Karatzas and H. Wang,\n                      Connection between bounded\u2010variation control and Dynkin games\n                      , in Optimal Control and Partial Differential Equations, J. L. Menaldi, E. Rofman, and A. Sulem, eds., IOS Press, Amsterdam, 2001, pp. 363\u2013373."},{"key":"R11","unstructured":"T. Kawabata,\n                      On a Singular Control Problem for a Time Changed Distorted Brownian Motion,\n                      doctoral thesis, Graduate School of Engineering Science, Osaka University, Japan, 1998."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013527"},{"key":"R13","unstructured":"P.Meyer, Un cours sur les int\u00e9grales stochastiques, Springer, Berlin, 1976, 0\u20130, 245\u2013400. Lecture Notes in Math., Vol. 51158:18721"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/03020303"},{"key":"R15","first-page":"4413","volume":"258","author":"Stampacchia Guido","year":"1964","journal-title":"C. R. Acad. Sci. Paris"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1287\/moor.10.1.63"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.32917\/hmj\/1206135203"},{"key":"R18","first-page":"185","volume":"4","author":"Zabczyk J.","year":"1984","journal-title":"Probab. Math. Statist."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012901387136","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:32:53Z","timestamp":1787319173000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012901387136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0363012901387136"],"URL":"https:\/\/doi.org\/10.1137\/s0363012901387136","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}