Keywords
- Weak Convergence
- Infinitesimal Generator
- Contraction Semigroup
- Martingale Problem
- Integrable Martingale
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References
J. S. Baras, A. La Vigna, "Expert systems and VLSI architectures for real-time non-Gaussian detectors and filters", in C. Byrnes and A. Lindquist eds., Proceedings of MTNS-85, North-Holland, to appear.
Ya. I. Belopol'skaya, Z. I. Nagolkina, "On a class of stochastic partial differential equations," Th. of Prob. and its Appl., 27, 592–599, 1982.
P. Billingsley, Convergence of Probability Measures, John Wiley, New York, 1968.
P. Billingsley, Weak Convergence of Measures: Applications in Probability, SIAM, Philadelphia, 1971.
J. M. C. Clark, "The design of robust approximations to the stochastic differential equations of nonlinear filtering," in J. K. Skwirzynski ed., Communication Systems and Random Process Theory, Sijthoff and Noordhoff, Aalpen aan den Rijn, 1978.
E. B. Dynkin, Markov Processes — I, Springer-Verlag, Berlin, 1965.
A. Germani, M. Piccioni, "A Galerkin approximation for the Zakai equation," in P. Thoft-Christensen, ed., Systems Modelling and Optimization, Springer-Verlag, Berlin, 1984.
I. I. Gihman, A. V. Skorohod, The Theory of Stochastic Processes, III, Springer-Verlag, New York, 1979.
E. Hille, Functional Analysis and Semigroups, AMS, New York, 1948.
J. Jacod, Calcul Stochastique et Problémes de Martingales, Springer-Verlag, Berlin, 1977.
G. Kallianpur, C. Striebel, "Estimation of stochastic systems: arbitrary system process with additive white noise observation errors," Ann. Math. Stat., 39, 785–801, 1968.
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1976.
T. G. Kurtz, "Extensions of Trotter's operator semigroup approximation theorems," J. Funct. Anal., 3, 354–375, 1969.
T. G. Kurtz, "Semigroups of conditional shifts and approximations of Markov processes." Ann. Prob., 4, 618–642, 1975.
T. G. Kurtz, Approximation of Population Processes, SIAM, Philadelphia, 1981.
H. J. Kushner, Probability Methods for Approximation in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977.
H. J. Kushner, "A robust discrete state approximation to the optimal nonlinear filter for a diffusion," Stochastics, 3, 75–83, 1979.
H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes, MIT, Cambridge, 1984.
H. J. Kushner, H. Huang, "Approximate and limit results for nonlinear filters with wide bandwidth observation noise," Report LCDS 84-36, 1984.
F. Legland, "Estimation de paramètres dans les processus stochastiques en observation incomplète," Thèse, Université Paris IX, 1981.
T. Lindvall, "Weak convergence of probability measures and random functions in the function space D[0,∞)," J. Appl. Prob., 10, 109–121, 1973.
P.-A. Meyer, Martingales and Stochastic Integrals I, Springer-Verlag, Berlin, 1978.
M. Metivier, Semimartingales, W. de Gruyter, Berlin, 1982.
R. D. Richtmyer, K. W. Morton, Difference Methods for Initial-Value Problems, Interscience, New York, 1967.
B. Stewart, "Generation of analytic semigroups by strongly elliptic operators," Trans. Amer. Math. Soc., 199, 141–162, 1974.
D. W. Stroock, S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979.
H. Trotter, "Approximation of semigroups of operators," Pacific J. Math., 8, 887–919, 1958.
H. Trotter, "On the product of semigroups of operators," Proc. Amer. Math. Soc., 10, 545–551, 1959.
D. Williams, Diffusions, Markov Processes and Martingales, Vol. 1, John Wiley, Chichester, 1979.
K. Yosida, Functional Analysis, Springer-Verlag, Berlin, 1968.
M. Zakai, "On the optimal filtering of diffusion processes," Z. Wahr. verw. Geb., 11, 230–243, 1969.
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© 1987 Springer-Verlag
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Piccioni, M. (1987). Convergence of implicit discretization schemes for linear differential equations with application to filtering. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications. Lecture Notes in Mathematics, vol 1236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072892
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DOI: https://doi.org/10.1007/BFb0072892
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