{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T08:32:16Z","timestamp":1726043536516},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030222840"},{"type":"electronic","value":"9783030222857"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-22285-7_8","type":"book-chapter","created":{"date-parts":[[2019,8,31]],"date-time":"2019-08-31T07:28:09Z","timestamp":1567236489000},"page":"221-260","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Unbiased It\u00f4 Type Stochastic Representation for Transport PDEs: A Toy Example"],"prefix":"10.1007","author":[{"given":"Gon\u00e7alo","family":"dos Reis","sequence":"first","affiliation":[]},{"given":"Greig","family":"Smith","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,1]]},"reference":[{"key":"8_CR1","unstructured":"Agarwal, A., Claisse, J.: Branching diffusion representation of quasi-linear elliptic PDEs and estimation using Monte Carlo method. arXiv preprint \n                  arXiv:1704.00328\n                  \n                 (2017)"},{"issue":"3","key":"8_CR2","doi-asserted-by":"publisher","first-page":"2028","DOI":"10.3150\/16-BEJ803","volume":"23","author":"P Andersson","year":"2017","unstructured":"Andersson, P., Kohatsu-Higa, A.: Unbiased simulation of stochastic differential equations using parametrix expansions. Bernoulli 23(3), 2028\u20132057 (2017)","journal-title":"Bernoulli"},{"key":"8_CR3","doi-asserted-by":"crossref","unstructured":"Bernal, F., dos Reis, G., Smith, G.: Hybrid PDE solver for data-driven problems and modern branching. Eur. J. Appl. Math. 1\u201324 (2017)","DOI":"10.1017\/S0956792517000109"},{"issue":"5","key":"8_CR4","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1051\/m2an\/2010054","volume":"44","author":"Dan Crisan","year":"2010","unstructured":"Crisan, D., Manolarakis, K.: Probabilistic methods for semilinear partial differential equations. Applications to finance. Math. Model. Numer. Anal. 44(5), 1107 (2010)","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"8_CR5","unstructured":"Cuchiero, C., Teichmann, J.: Stochastic representations of ordinary differential equations via affine processes. Working paper (2017)"},{"key":"8_CR6","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1051\/ps\/2017001","volume":"21","author":"Mahamadou Doumbia","year":"2017","unstructured":"Doumbia, M., Oudjane, N., Warin, X.: Unbiased monte carlo estimate of stochastic differential equations expectations. ESAIM: Probab. Statis. 21, 56\u201387 (2017)","journal-title":"ESAIM: Probability and Statistics"},{"key":"8_CR7","unstructured":"Evans, L.C.: Partial Differential Equations. American Mathematical Society, Providence, R.I. (1998)"},{"issue":"4","key":"8_CR8","doi-asserted-by":"publisher","first-page":"1322","DOI":"10.1214\/10-AAP723","volume":"21","author":"Arash Fahim","year":"2011","unstructured":"Fahim, A., Touzi, N., Warin, X.: A probabilistic numerical method for fully nonlinear parabolic PDEs. Ann. Appl. Probab. 1322\u20131364 (2011)","journal-title":"The Annals of Applied Probability"},{"issue":"4","key":"8_CR9","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s007800050068","volume":"3","author":"E Fourni\u00e9","year":"1999","unstructured":"Fourni\u00e9, E., Lasry, J.-M., Lebuchoux, J., Lions, P.-L., Touzi, N.: Applications of malliavin calculus to monte carlo methods in finance. Financ. Stochast. 3(4), 391\u2013412 (1999)","journal-title":"Financ. Stochast."},{"key":"8_CR10","unstructured":"Han, J., Jentzen, A., Weinan, E.: Overcoming the curse of dimensionality: solving high-dimensional partial differential equations using deep learning. arXiv preprint \n                  arXiv:1707.02568\n                  \n                 (2017)"},{"key":"8_CR11","doi-asserted-by":"crossref","unstructured":"Henry-Labordere, P.: Counterparty risk valuation: a marked branching diffusion approach. SSRN 1995503 (2012)","DOI":"10.2139\/ssrn.1995503"},{"issue":"1","key":"8_CR12","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1214\/17-AIHP880","volume":"55","author":"Pierre Henry-Labord\u00e8re","year":"2019","unstructured":"Henry-Labordere, P., Oudjane, N., Tan, X., Touzi, N., Warin, X., et al.: Branching diffusion representation of semilinear PDEs and Monte Carlo approximation. In: Annales de l\u2019Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques, vol. 55(1), pp. 184\u2013210, Institut Henri Poincar\u00e9 (2019)","journal-title":"Annales de l'Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques"},{"key":"8_CR13","unstructured":"Henry-Labordere, P., Touzi, N.: Branching diffusion representation for nonlinear Cauchy problems and Monte Carlo approximation. arXiv preprint \n                  arXiv:1801.08794\n                  \n                 (2018)"},{"issue":"2","key":"8_CR14","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1016\/j.spa.2013.10.005","volume":"124","author":"P Henry-Labordere","year":"2014","unstructured":"Henry-Labordere, P., Tan, X., Touzi, N.: A numerical algorithm for a class of BSDEs via the branching process. Stochast. Process. Appl. 124(2), 1112\u20131140 (2014)","journal-title":"Stochast. Process. Appl."},{"issue":"6","key":"8_CR15","doi-asserted-by":"publisher","first-page":"3305","DOI":"10.1214\/17-AAP1281","volume":"27","author":"P Henry-Labordere","year":"2017","unstructured":"Henry-Labordere, P., Tan, X., Touzi, N.: Unbiased simulation of stochastic differential equations. Ann. Appl. Probab. 27(6), 3305\u20133341 (2017)","journal-title":"Ann. Appl. Probab."},{"issue":"3","key":"8_CR16","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF00280740","volume":"58","author":"T Kato","year":"1975","unstructured":"Kato, T.: The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58(3), 181\u2013205 (1975)","journal-title":"Arch. Rational Mech. Anal."},{"issue":"6","key":"8_CR17","doi-asserted-by":"publisher","first-page":"1118","DOI":"10.1016\/j.matcom.2009.12.009","volume":"80","author":"A Rasulov","year":"2010","unstructured":"Rasulov, A., Raimova, G., Mascagni, M.: Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation. Math. Comput. Simul. 80(6), 1118\u20131123 (2010)","journal-title":"Math. Comput. Simul."},{"key":"8_CR18","unstructured":"Warin, X.: Variations on branching methods for nonlinear PDEs. \n                  arXiv:1701.07660\n                  \n                 (2017)"},{"key":"8_CR19","doi-asserted-by":"crossref","unstructured":"Warin, X.: Monte Carlo for high-dimensional degenerated semi linear and full non linear PDEs. arXiv preprint \n                  arXiv:1805.05078\n                  \n                 (2018)","DOI":"10.1515\/mcma-2018-2020"},{"key":"8_CR20","doi-asserted-by":"crossref","unstructured":"Williams, D.: Probability with martingales. Cambridge University Press (1991)","DOI":"10.1017\/CBO9780511813658"}],"container-title":["Springer Proceedings in Mathematics &amp; Statistics","Frontiers in Stochastic Analysis\u2013BSDEs, SPDEs and their Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-22285-7_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,31]],"date-time":"2019-08-31T07:31:05Z","timestamp":1567236665000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-22285-7_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030222840","9783030222857"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-22285-7_8","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"1 September 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"BSDE-SPDE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on BSDEs","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Edinburgh","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 July 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 July 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"bsdespde2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}