{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T20:12:53Z","timestamp":1786997573731,"version":"build-2736575974"},"reference-count":39,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Theoretical Population Biology"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1016\/j.tpb.2024.07.003","type":"journal-article","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T12:29:14Z","timestamp":1724329754000},"page":"59-73","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["Duality and the well-posedness of a martingale problem"],"prefix":"10.1016","volume":"159","author":[{"given":"Andrej","family":"Depperschmidt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Greven","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6421-5460","authenticated-orcid":false,"given":"Peter","family":"Pfaffelhuber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.tpb.2024.07.003_b1","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1214\/EJP.v15-741","article-title":"A new model for evolution in a spatial continuum","volume":"15","author":"Barton","year":"2010","journal-title":"Electron. J. Probab."},{"issue":"01","key":"10.1016\/j.tpb.2024.07.003_b2","doi-asserted-by":"crossref","first-page":"P01002","DOI":"10.1088\/1742-5468\/2013\/01\/P01002","article-title":"Modelling evolution in a spatial continuum","volume":"2013","author":"Barton","year":"2013","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"10.1016\/j.tpb.2024.07.003_b3","series-title":"Harmonic Analysis on Semigroups","volume":"vol. 100","author":"Berg","year":"1984"},{"issue":"3","key":"10.1016\/j.tpb.2024.07.003_b4","doi-asserted-by":"crossref","first-page":"685","DOI":"10.4171\/jems\/264","article-title":"Potential-theoretical methods in the construction of measure-valued Markov branching processes","volume":"13","author":"Beznea","year":"2011","journal-title":"J. Eur. Math. Soc. (JEMS)"},{"key":"10.1016\/j.tpb.2024.07.003_b5","doi-asserted-by":"crossref","first-page":"2246","DOI":"10.1214\/aop\/1176989019","article-title":"Invariant measures and evolution equations for Markov processes","volume":"21","author":"Bhatt","year":"1993","journal-title":"Ann. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b6","series-title":"Rare mutations in the spatial Lambda-Fleming-Viot model in a fluctuating environment and superbrownian motion","author":"Chetwynd-Diggle","year":"2019"},{"key":"10.1016\/j.tpb.2024.07.003_b7","series-title":"\u00c9cole d\u2019\u00c9t\u00e9 de Probabilit\u00e9s de Saint-Flour XXI\u20141991","first-page":"1","article-title":"Measure-valued Markov processes","volume":"vol. 1541","author":"Dawson","year":"1993"},{"issue":"7","key":"10.1016\/j.tpb.2024.07.003_b8","first-page":"2277","article-title":"Equilibria and quasiequilibria for infinite collections of interacting Fleming-Viot processes","volume":"347","author":"Dawson","year":"1995","journal-title":"Trans. Amer. Math. Soc."},{"issue":"3","key":"10.1016\/j.tpb.2024.07.003_b9","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1214\/009117905000000747","article-title":"Skew convolution semigroups and affine Markov processes","volume":"34","author":"Dawson","year":"2006","journal-title":"Ann. Probab."},{"issue":"454","key":"10.1016\/j.tpb.2024.07.003_b10","first-page":"iv+179","article-title":"Historical processes","volume":"93","author":"Dawson","year":"1991","journal-title":"Mem. Amer. Math. Soc."},{"key":"10.1016\/j.tpb.2024.07.003_b11","series-title":"Genealogy-valued feller diffusion","author":"Depperschmidt","year":"2023"},{"issue":"6","key":"10.1016\/j.tpb.2024.07.003_b12","doi-asserted-by":"crossref","first-page":"2560","DOI":"10.1214\/11-AAP831","article-title":"Tree-valued Fleming-Viot dynamics with mutation and selection","volume":"22","author":"Depperschmidt","year":"2012","journal-title":"Ann. Appl. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b13","series-title":"Stochastic Processes","author":"Doob","year":"1953"},{"issue":"3","key":"10.1016\/j.tpb.2024.07.003_b14","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1214\/aop\/1176989116","article-title":"Superprocesses and partial differential equations","volume":"21","author":"Dynkin","year":"1993","journal-title":"Ann. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b15","series-title":"An Introduction to Superprocesses","volume":"vol. 20","author":"Etheridge","year":"2000"},{"key":"10.1016\/j.tpb.2024.07.003_b16","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1214\/17-EJP61","article-title":"The Brownian net and selection in the spatial \u039b-fleming-viot process","volume":"22","author":"Etheridge","year":"2017","journal-title":"Electron. J. Probab."},{"issue":"4","key":"10.1016\/j.tpb.2024.07.003_b17","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1214\/18-AOP1266","article-title":"Genealogical constructions of population models","volume":"47","author":"Etheridge","year":"2019","journal-title":"Ann. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b18","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1214\/20-EJP523","article-title":"Rescaling limits of the spatial Lambda-Fleming-Viot process with selection","volume":"25","author":"Etheridge","year":"2020","journal-title":"Electron. J. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b19","series-title":"Markov Processes","author":"Ethier","year":"1986"},{"issue":"3","key":"10.1016\/j.tpb.2024.07.003_b20","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/S0246-0203(97)80095-7","article-title":"Coalescing Markov labelled partitions and a continuous sites genetics model with infinitely many types","volume":"33","author":"Evans","year":"1997","journal-title":"Ann. Inst. H. Poincar\u00e9 Probab. Statist."},{"issue":"4","key":"10.1016\/j.tpb.2024.07.003_b21","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1214\/aop\/1041903211","article-title":"Cluster formation in a stepping-stone model with continuous, hierarchically structured sites","volume":"24","author":"Evans","year":"1996","journal-title":"Ann. Probab."},{"issue":"1","key":"10.1016\/j.tpb.2024.07.003_b22","first-page":"43","article-title":"Renormalisation of hierarchically interacting cannings processes","volume":"11","author":"Greven","year":"2014","journal-title":"ALEA Lat. Am. J. Probab. Math. Stat."},{"key":"10.1016\/j.tpb.2024.07.003_b23","series-title":"Ancestral web and measure-valued path representations","author":"Greven","year":"2023"},{"issue":"1\u20132","key":"10.1016\/j.tpb.2024.07.003_b24","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s00440-008-0169-3","article-title":"Convergence in distribution of random metric measure spaces (\u039b-coalescent measure trees)","volume":"145","author":"Greven","year":"2009","journal-title":"Probab. Theory Related Fields"},{"issue":"3\u20134","key":"10.1016\/j.tpb.2024.07.003_b25","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1007\/s00440-012-0413-8","article-title":"Tree-valued resampling dynamics martingale problems and applications","volume":"155","author":"Greven","year":"2013","journal-title":"Probab. Theory Related Fields"},{"key":"10.1016\/j.tpb.2024.07.003_b26","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1214\/16-EJP4514","article-title":"Continuum space limit of the genealogies of interacting Fleming-Viot processes on Z","volume":"21","author":"Greven","year":"2016","journal-title":"Electron. J. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b27","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1214\/12-PS206","article-title":"On the notion(s) of duality for Markov processes","volume":"11","author":"Jansen","year":"2014","journal-title":"Probab. Surv."},{"key":"10.1016\/j.tpb.2024.07.003_b28","article-title":"Foundations of modern probability","volume":"vol. 99","author":"Kallenberg","year":"2021"},{"key":"10.1016\/j.tpb.2024.07.003_b29","series-title":"Brownian Motion and Stochastic Calculus","author":"Karatzas","year":"1991"},{"issue":"2","key":"10.1016\/j.tpb.2024.07.003_b30","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF00320919","article-title":"Stochastic partial differential equations for some measure-valued diffusions","volume":"79","author":"Konno","year":"1988","journal-title":"Probab. Theory Related Fields"},{"issue":"17","key":"10.1016\/j.tpb.2024.07.003_b31","first-page":"52","article-title":"Stationary solutions and forward equations for controlled and singular martingale problems","volume":"6","author":"Kurtz","year":"2001","journal-title":"Electron. J. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b32","first-page":"207","article-title":"Convergence in distribution of stochastic processes","volume":"2","author":"LeCam","year":"1957","journal-title":"Univ. Calif. Publ. Statist."},{"key":"10.1016\/j.tpb.2024.07.003_b33","series-title":"Interacting Particle Systems","volume":"vol. 276","author":"Liggett","year":"1985"},{"key":"10.1016\/j.tpb.2024.07.003_b34","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1214\/16-ECP17","article-title":"Boundedly finite measures: Separation and convergence by an algebra of functions","volume":"21","author":"L\u00f6hr","year":"2016","journal-title":"Electron. Commun. Probab."},{"key":"10.1016\/j.tpb.2024.07.003_b35","series-title":"Growth properties of the infinite-parent spatial Lambda-Fleming Viot process","author":"Louvet","year":"2022"},{"issue":"4","key":"10.1016\/j.tpb.2024.07.003_b36","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/BF01198848","article-title":"Stochastic p.d.e.\u2019s arising from the long range contact and long range voter processes","volume":"102","author":"M\u00fcller","year":"1995","journal-title":"Probab. Theory Related Fields"},{"key":"10.1016\/j.tpb.2024.07.003_b37","series-title":"Bernstein Functions","volume":"vol. 37","author":"Schilling","year":"2012"},{"key":"10.1016\/j.tpb.2024.07.003_b38","series-title":"Two contrasting properties of solutions for one-dimensional stochastic partial differential equations","first-page":"415","author":"Shiga","year":"1994"},{"issue":"2","key":"10.1016\/j.tpb.2024.07.003_b39","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1214\/13-AIHP571","article-title":"The spatial Lambda-Fleming-Viot process: An event-based construction and a lookdown representation","volume":"51","author":"V\u00e9ber","year":"2015","journal-title":"Ann. Inst. Henri Poincar\u00e9 Probab. Stat."}],"container-title":["Theoretical Population Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0040580924000765?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0040580924000765?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T23:03:40Z","timestamp":1726268620000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0040580924000765"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10]]},"references-count":39,"alternative-id":["S0040580924000765"],"URL":"https:\/\/doi.org\/10.1016\/j.tpb.2024.07.003","relation":{},"ISSN":["0040-5809"],"issn-type":[{"value":"0040-5809","type":"print"}],"subject":[],"published":{"date-parts":[[2024,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Duality and the well-posedness of a martingale problem","name":"articletitle","label":"Article Title"},{"value":"Theoretical Population Biology","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.tpb.2024.07.003","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2024 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}]}}