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References
F. Allinger-S. Mitter; New results on the innovations problem for non-linear filtering, Stochastics 4, 339–348 (1981).
J. M. Bismut; Martingales, the Malliavin calculus and Hypoellipticity under general Hörmander's conditions, Z. Wahrscheilichkeitstheorie verw. Gebiete 56, 469–505 (1981).
J. M. Bismut-D. Michel; Diffusions conditionelles, to appear.
R.S. Bucy-D.D. Joseph; Filtering for stochastic processes with applications to guidance, Interscience, 1968.
J. M. C. Clark; Contribution for the one-to-one correspondence between an observation process and its innovation, Center for computing and automation, Imperial College, London Tech. Rep. 1, 1969.
M. Fujisaki-G. Kallianpur-H. Kunita; Stochastic differential equations for the non linear filtering problem, Osaka J. Math. 9, 19–40 (1972).
T. Funaki; Construction of a solution of random transport equation with boundary condition, J. Math. Soc. Japan 31, 719–744 (1979).
L. Hörmander; Hypoelliptic second order differential equations, Acta Math. 119, 147–171 (1969).
W. Ikeda-S. Watanabe; Stochastic differential equations and diffusion processes, North-Holland, Kodansha, 1981.
K. Itô; Multiple Wiener integral, J. Math. Soc. Japan 3, 157–169 (1951).
T. Kailath; An innovation approach to least squares estimation, Part I; Linear filtering with additive white noise, IEEE Trans. Automatic Control, AC-13, 6, 646–655 (1968).
G. Kallianpur; Stochastic filtering theory, Springer-Verlag, 1980.
N. V. Krylov-B. L. Rozovsky; On the Cauchy problem for linear stochastic partial differential equations, Izv. Akad. Nauk. SSSR 41, 1329–1347 (1977), English transl. Math USSR Izvestija 11, 1267–1284 (1977).
H. Kunita; On the decomposition of solutions of stochastic differential equations, Proceedings, LMS Durham Symposium, 1980, Lecture Notes in Math 851, 213–255 (1981).
H. Kunita; On backward stochastic differential equations, Stochastics, submitted.
H. Kunita; Cauchy problem for stochastic partial differential equations arizing in non linear filtering theory, Systems and Control letters, 1, 37–41 (1981).
H. Kunita; Densities of measure-valued process governed by a stochastic partial differential equation, Systems and Control letters, to appear.
H. Kunita-S. Watanabe; On square integrable martingales, Nagoya Math. J. 30, 209–245 (1967).
H. Kushner; Dynamical equations for optimal non linear filtering, J. Differential Equations 3, 179–190 (1967).
R. Sh. Liptser-A. N. Shiryayev; Statistics of Random Processes I, Springer-Verlag, New York, 1977.
P. Malliavin; Stochastic calculus of variation and hypoelliptic operators, Proc. Intern. Sysmp. SDE Kyoto 1976, Kinokuniya Tokyo, 195–263 (1978).
D. Michel; Regularité des lois conditionnelles en théorie du filtrage non-linéaire et calcul des variations stochastique, J. of Funct. An. 41, 8–36 (1981).
P. A. Meyer; Un cours sur les intégrales stochastiques, Séminaire de Probabilités X, Lecture Notes in Math. 511, 245–400 (1976).
S. Ogawa; A partial differential equation with the white noise as a coefficient, Z. Wahrscheinlichkeitstheorie verw.Gebiete 28, 53–71 (1973).
E. Pardoux; Stochastic partial differential equations and filtering of diffusion processes, Stochastics 3, 127–167 (1979).
B. L. Rozovsky-A. Shimizu; Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density, Nagoya Math. J. 84, to appear.
D. W. Stroock; The Malliavin calculus and its application to second order parabolic differential equations; Part I & II, Math. Systems Theory 14, 25–65 (1981), 141–171 (1981).
D. W. Stroock-S. R. S. Varadhan; Multidimensional Diffusion Processes, Springer-Verlag, 1979.
A. Ju. Veretennikov-N. V. Krylov; On explicit formula for solutions of stochastic equation, Math. Sbornik 100 (142), 266–284 (1976); English transl. Math Sbornik 29, 239–256 (1976).
M. Zakai; On the optimal filtering of diffusion processes, Z. Wahrscheinlichkeitstheorie yerw Gebiete 11, 230–243 (1969).
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Kunita, H. (1982). Stochastic partial differential equations connected with non-linear filtering. In: Mitter, S.K., Moro, A. (eds) Nonlinear Filtering and Stochastic Control. Lecture Notes in Mathematics, vol 972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064861
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DOI: https://doi.org/10.1007/BFb0064861
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