{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T16:36:21Z","timestamp":1717259781071},"reference-count":43,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this article, we are interested in solving numerically backward doubly stochastic differential equations (BDSDEs) with random terminal time \u03c4. The main motivations are giving a probabilistic representation of the Sobolev\u2019s solution of Dirichlet problem for semilinear SPDEs and providing the numerical scheme for such SPDEs. Thus, we study the strong approximation of this class of BDSDEs when \u03c4 is the first exit time of a forward SDE from a cylindrical domain. Euler schemes and bounds for the discrete-time approximation error are provided.<\/jats:p>","DOI":"10.1515\/mcma-2016-0111","type":"journal-article","created":{"date-parts":[[2016,8,10]],"date-time":"2016-08-10T09:56:29Z","timestamp":1470822989000},"page":"229-258","source":"Crossref","is-referenced-by-count":2,"title":["Numerical computation for backward doubly SDEs with random terminal time"],"prefix":"10.1515","volume":"22","author":[{"given":"Anis","family":"Matoussi","sequence":"first","affiliation":[{"name":"University of Maine, Risk and Insurance Institute of Le Mans, Laboratoire Manceau de Math\u00e9matiques, Avenue Olivier Messiaen, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wissal","family":"Sabbagh","sequence":"additional","affiliation":[{"name":"University of Maine, Risk and Insurance Institute of Le Mans, Laboratoire Manceau de Math\u00e9matiques, Avenue Olivier Messiaen, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,8,5]]},"reference":[{"key":"2023040101594993602_j_mcma-2016-0111_ref_001_w2aab2b8e1858b1b7b1ab2b1b1Aa","unstructured":"Aboura O.,\nOn the discretization of backward doubly stochastic differential equations,\npreprint 2009, https:\/\/arxiv.org\/pdf\/1302.0440.pdf."},{"key":"2023040101594993602_j_mcma-2016-0111_ref_002_w2aab2b8e1858b1b7b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"Aman A.,\nA numerical scheme for backward doubly stochastic differential equations,\nBernoulli 19 (2013), no. 1, 93\u2013114.","DOI":"10.3150\/11-BEJ391"},{"key":"2023040101594993602_j_mcma-2016-0111_ref_003_w2aab2b8e1858b1b7b1ab2b1b3Aa","unstructured":"Bachouch A.,\nNumerical computations for backward doubly stochastic differential equations and non-linear stochastic PDEs,\nPh.D. thesis, Universit\u00e9 du Maine, Le Mans, 2014."},{"key":"2023040101594993602_j_mcma-2016-0111_ref_004_w2aab2b8e1858b1b7b1ab2b1b4Aa","doi-asserted-by":"crossref","unstructured":"Bachouch A., Gobet E. and Matoussi A.,\nEmpirical regression method for backward doubly stochastic differential equations,\nSIAM\/ASA J. Uncertain. Quantif. 4 (2016), no. 1, 358\u2013379.","DOI":"10.1137\/15M1022094"},{"key":"2023040101594993602_j_mcma-2016-0111_ref_005_w2aab2b8e1858b1b7b1ab2b1b5Aa","unstructured":"Bachouch A., Gobet E. and Matoussi A.,\nNumerical computation for quasilinear SPDEs via generalized backward doubly SDEs,\nforthcoming paper."},{"key":"2023040101594993602_j_mcma-2016-0111_ref_006_w2aab2b8e1858b1b7b1ab2b1b6Aa","unstructured":"Bachouch A., Lasmar A. B., Matoussi A. and Mnif M.,\nNumerical scheme for semilinear SPDEs via backward doubly SDEs,\nStoch. Partial Differ. Equ. Anal. Comput. 1 (2016), 1\u201343."},{"key":"2023040101594993602_j_mcma-2016-0111_ref_007_w2aab2b8e1858b1b7b1ab2b1b7Aa","doi-asserted-by":"crossref","unstructured":"Bally V.,\nConstruction of asymptotically optimal controls for control and game problems,\nProbab. 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