{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:15:49Z","timestamp":1787321749931,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The aim of this paper is twofold. First we analyze the sequence of intensity measures of a spatial branching point process arising in a multiple-target tracking context. We study its stability properties, characterize its long time behavior, and provide a series of weak Lipschitz-type functional contraction inequalities. Second we design and analyze an original particle scheme to approximate numerically these intensity measures. Under appropriate regularity conditions, we obtain uniform and nonasymptotic estimates and a functional central limit theorem. To the best of our knowledge, these are the first sharp theoretical results available for this class of spatial branching point processes.<\/jats:p>","DOI":"10.1137\/100788987","type":"journal-article","created":{"date-parts":[[2011,8,4]],"date-time":"2011-08-04T18:06:08Z","timestamp":1312481168000},"page":"1766-1792","source":"Crossref","is-referenced-by-count":3,"title":["Particle Approximation of the Intensity Measures of a Spatial Branching Point Process Arising in Multitarget Tracking"],"prefix":"10.1137","volume":"49","author":[{"given":"Francois","family":"Caron","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Del Moral","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnaud","family":"Doucet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michele","family":"Pace","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,8,4]]},"reference":[{"key":"R1","first-page":"2130","volume":"14","author":"Bercu B.","year":"2009","journal-title":"Electron. J. Probab.","ISSN":"https:\/\/id.crossref.org\/issn\/1083-6489","issn-type":"print"},{"key":"R2","unstructured":"F. Caron, P. Del Moral, M. Pace, and B.N. Vo,\n                      On the Stability and Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering\n                      , Technical report 7376, INRIA, 2010."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"F. C\u00e9rou, P. Del Moral, and A. Guyader,\n                      A non asymptotic variance theorem for unnormalized Feynman-Kac particle models\n                      , Ann. Inst. H. Poincar\u00e9, to appear (2011).","DOI":"10.1214\/10-AIHP358"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"P. Del Moral,\n                      Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications\n                      , Probab. Appl. (N.Y.), Springer-Verlag, New York, 2004.","DOI":"10.1007\/978-1-4684-9393-1"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"P. Del Moral, A. Doucet, and A. Jasra,\n                      On adaptive resampling procedures for sequential Monte Carlo methods\n                      , Bernoulli, to appear (2011).","DOI":"10.3150\/10-BEJ335"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"P. Del Moral and E. Rio,\n                      Concentration inequalities for mean field particle models\n                      , Ann. Appl. Probab., to appear (2011).","DOI":"10.1214\/10-AAP716"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. Doucet, J. F. G. De Freitas, and N. J. Gordon,\n                      Sequential Monte Carlo Methods in Practice\n                      , Springer-Verlag, New York, 2001.","DOI":"10.1007\/978-1-4757-3437-9"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"J. Goutsias, R. Mahler, and H. Nguyen, eds.\n                      Random Sets Theory and Applications\n                      , Springer-Verlag, New York, 1997.","DOI":"10.1007\/978-1-4612-1942-2"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"I. Goodman, R. Mahler, and H. Nguyen,\n                      Mathematics of Data Fusion\n                      , Kluwer Academic, Dordrecht, The Netherlands, 1997.","DOI":"10.1007\/978-94-015-8929-1"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-006-8552-y"},{"key":"R11","unstructured":"R. Mahler,\n                      A theoretical foundation for the Stein-Winter Probability Hypothesis Density (PHD) multi-target tracking approach\n                      , in Proceedings of the 2002 Military Sensing Symposia (MSS) National Symposium on Sensor and Data Fusion, Vol. I, San Antonio, TX, 2002."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.2003.1261119"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"S. Mori and C.Y. Chong,\n                      Point process formalism for multiple target tracking\n                      , in Proceedings of the 5th International Conference on Information Fusion, 2002, pp. 10\u201317.","DOI":"10.1109\/ICIF.2002.1021125"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1986.1104306"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/070710457"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2006.881190"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.2005.1561884"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100788987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:14:44Z","timestamp":1787318084000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100788987"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100788987"],"URL":"https:\/\/doi.org\/10.1137\/100788987","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}