The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


    Ballantyne, D.J.; Chan, H.Y.; Kouritzin, M.A. A novel branching particle method for tracking. Signal and Data Processing of Small Targets 2000, Proceedings of SPIE 4048 (2000), 277-287.

    Bass, R.F.; Hsu, P. Some potential theory for reflecting Brownian motion in Hˆlder and Lipschitz domains. Ann. Probab. 19 (1991), no. 2, 486--508. MR1106272 (92i:60142)

    Budhiraja, A. Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter. Ann. Inst. H. PoincarÈ Probab. Statist. 39 (2003), no. 6, 919--941. MR2010391 (2004h:60063)

    Budhiraja, A.; Kushner, H.J. Approximation and limit results for nonlinear filters over an infinite time interval. SIAM J. Control Optim. 37 (1999), no. 6, 1946--1979. MR1720146 (2000i:93080)

    Budhiraja, A.; Kushner, H.J. Approximation and limit results for nonlinear filters over an infinite time interval. II. Random sampling algorithms. SIAM J. Control Optim. 38 (2000), no. 6, 1874--1908. MR1776660 (2001f:93070)

    Budhiraja, A.; Kushner, H.J. Monte Carlo algorithms and asymptotic problems in nonlinear filtering. Stochastics in finite and infinite dimensions, 59--87, Trends Math., Birkh‰user Boston, Boston, MA, 2001. MR1797081 (2001i:93120)

    Chow, P.L.; Khasminskii, R.; Liptser, R. Tracking of signal and its derivatives in Gaussian white noise. Stochastic Process. Appl. 69 (1997), no. 2, 259--273. MR1472954 (98m:60065)

    Chow, P.L.; Khasminskii, R.; Liptser, R. On estimation of time dependent spatial signal in Gaussian white noise. Stochastic Process. Appl. 96 (2001), no. 1, 161--175. MR1856685 (2002k:62051)

    Davies, E.B. Heat kernels and spectral theory. Cambridge Tracts in Mathematics, 92. Cambridge University Press, Cambridge, 1989. x+197 pp. ISBN: 0-521-36136-2 MR0990239 (90e:35123)

    Elliott R.J. Financial Filtering. Lecture Note.

    Freidlin, M. Functional integration and partial differential equations. Annals of Mathematics Studies, 109. Princeton University Press, Princeton, NJ, 1985. x+545 pp. ISBN: 0-691-08354-1; 0-691-08362-2 MR0833742 (87g:60066)

    Fukushima, M.; Oshima, Y.; Takeda, M. Dirichlet forms and symmetric Markov processes. de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 1994. x+392 pp. ISBN: 3-11-011626-X MR1303354 (96f:60126)

    Fukushima, M.; Tomisaki, M. Construction and decomposition of reflecting diffusions on Lipschitz domains with Hˆlder cusps. Probab. Theory Related Fields 106 (1996), no. 4, 521--557. MR1421991 (98d:60157)

    Kouritzin, M.A.; Long, H.W.; Sun, W. Nonlinear filtering for diffusions in random environments. J. Theoret. Probab. 16 (2003), no. 1, 1--20. MR1956818

    Kouritzin, M.A.; RÈmillard B.; Chan, C. Parameter estimation for filtering problems with stable noise. Proceedings of 4th Annual Conference on Information Fusion I (2001) WeB127-WeB130.

    Kunita, H. Asymptotic behavior of the nonlinear filtering errors of Markov processes. J. Multivariate Anal. 1 (1971), 365--393. MR0301812 (46 #967)

    Kunita, H. Stochastic partial differential equations connected with nonlinear filtering. Nonlinear filtering and stochastic control (Cortona, 1981), 100--169, Lecture Notes in Math., 972, Springer, Berlin, 1982. MR0705933 (85e:60068)

    Kushner, H.J. Weak convergence methods and singularly perturbed stochastic control and filtering problems. Systems & Control: Foundations & Applications, 3. Birkh‰user Boston, Inc., Boston, MA, 1990. xviii+233 pp. ISBN: 0-8176-3437-1 MR1102242 (92d:93003)

    Ledoux, M. Logarithmic Sobolev inequalities for unbounded spin systems revisited. SÈminaire de ProbabilitÈs, XXXV, 167--194, Lecture Notes in Math., 1755, Springer, Berlin, 2001. MR1837286 (2002g:82001)

    Lototsky, S.; Mikulevicius, R.; Rozovskii, B.L. Nonlinear filtering revisited: a spectral approach. SIAM J. Control Optim. 35 (1997), no. 2, 435--461. MR1436632 (98a:60049)

    Ocone, D. Multiple integral expansions for nonlinear filtering. Stochastics 10 (1983), no. 1, 1--30. MR0714705 (85d:60083)

    Rosenblatt, M. Markov processes. Structure and asymptotic behavior. Die Grundlehren der mathematischen Wissenschaften, Band 184. Springer-Verlag, New York-Heidelberg, 1971. xiii+268 pp. MR0329037 (48 #7379)

    Tanaka, H. Diffusion processes in random environments. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Z¸rich, 1994), 1047--1054, Birkh‰user, Basel, 1995. MR1404004 (97g:60112)

    Zygmund, A. Trigonometric series. 2nd ed. Vols. I, II. Cambridge University Press, New York 1959 Vol. I. xii+383 pp.; Vol. II. vii+354 pp. MR0107776 (21 #6498)

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.