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Also, we discuss its relation to the operator-splitting method for the Zakai equation.<\/jats:p>","DOI":"10.1137\/s0363012998344270","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"893-915","source":"Crossref","is-referenced-by-count":25,"title":["Approximation of the Kushner Equation for Nonlinear Filtering"],"prefix":"10.1137","volume":"38","author":[{"given":"Kazufumi","family":"Ito","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boris","family":"Rozovskii","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"JohnBaras, Real time architectures for the Zakai equation and applications, Academic Press, Boston, MA, 1991, 15\u20133892g:94006","DOI":"10.1016\/B978-0-12-481005-1.50007-7"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"A. Bensoussan,\n                      Nonlinear filtering theory\n                      , in Progress in Automation and Information Systems, Recent Advances in Stochastic Calculus, J. S. Baras and V. Mirelli, eds., Springer\u2010Verlag, New York, 1990.","DOI":"10.1007\/978-1-4612-3408-1_2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0328074"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"J.Clark, The design of robust approximations to the stochastic differential equations of nonlinear filtering, Sijthoff & Noordhoff, Alphen aan den Rijn, 1978, 0\u20130, 721\u2013734. NATO Advanced Study Inst. Ser., Ser. E: Appl. Sci., No. 2558:26431","DOI":"10.1007\/978-94-011-7577-7_41"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(82)80044-3"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1080\/07362998908809174"},{"key":"R7","first-page":"19","volume":"9","author":"Fujisaki M.","year":"1972","journal-title":"Osaka J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0030-6126","issn-type":"print"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1080\/17442509108833704"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442185"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970838"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012993254783"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01084893"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(67)90023-X"},{"key":"R14","unstructured":"H. J. Kushner,\n                      Probability Methods for Approximations in Stochastic Control and for Elliptic Equations\n                      , Academic Press, New York, 1977."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0441-8"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012993248918"},{"key":"R17","first-page":"0","author":"Baranov V.","year":"1978","journal-title":"Vestnik Khar rime kov. Gos. Univ."},{"key":"R18","doi-asserted-by":"crossref","unstructured":"G.Marchuk, Splitting and alternating direction methods, Handb. Numer. Anal., I, North\u2010Holland, Amsterdam, 1990, 197\u20134621039325","DOI":"10.1016\/S1570-8659(05)80035-3"},{"key":"R19","unstructured":"\u00c9.Pardoux, Les \u00e9quations du filtrage non lin\u00e9aire des processus de diffusion, Travaux Rech. Coop. Programme 567, CNRS, Paris, 1983, 5\u20133686d:93123"},{"key":"R20","unstructured":"B. L. Rozovskii,\n                      Stochastic Evolution Systems, Linear Theory and Application to Nonlinear Filtering\n                      , Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991."},{"key":"R21","doi-asserted-by":"crossref","unstructured":"B.Rozovskii\u02d8, A simple proof of uniqueness for Kushner and Zakai equations, Academic Press, Boston, MA, 1991, 449\u201345892h:60065","DOI":"10.1016\/B978-0-12-481005-1.50029-6"},{"key":"R22","unstructured":"H. Tanabe,\n                      Equations of Evolution\n                      , Pitman, London, 1979."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012998344270","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:51:01Z","timestamp":1787230261000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012998344270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S0363012998344270"],"URL":"https:\/\/doi.org\/10.1137\/s0363012998344270","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}