Keywords
- Brownian Motion
- Conditional Statistic
- Optimal Filter
- Stochastic Calculus
- Stochastic Partial Differential Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Bardos and L. Tartar, Sur l'unicité des équations paraboliques et quelques questions voisines, Archive for Rational Mechanics and Analysis 50 (1973), 10–25.
J-M. Bismut and D. Michel, Diffusions conditionelles, J. Funct. Anal. 44 (1981), 174–211; 45 (1982), 274–282.
N. Bouleau and F. Hirsch, Propriétés d'absolue continuité dans les espace de Dirichlet et application aux équations différentielles stochastiques, in Seminaire de Probabilités XX, Lecture Notes in Math. 1204, Springer-Verlag (1986).
R. W. Brockett and J. M. C. Clark, On the geometry of the conditional density equation, in Analysis and Optimisation of Stochastic Systems, ed. by D. L. R. Jacobs, Academic Press(1980).
M. Chaleyat-Maurel, Robustesse en théorie du filtrage non linéaire et calcul des variations stochastique, C. R. A. S. Paris 297 (1983), 541–544.
M. Chaleyat-Maurel and D. Michel, Des Résultats de Non Existence de Filtre de Dimension Finie, Stochastics 13 (1984), 83–102.
S. D. Eidel'man, Parabolic Systems, North-Holland, Amsterdam, 1969.
G. Ferreyra, Smoothness of the unnormalized conditional measures of stochastic nonlinear filtering, Proceedings of the 23 rd IEEE Conference on Decision and Control, Las Vegas, 1984.
A. Friedman, Stochastic Partial Differential Equations and Applications, Academic Press, New York, 1975.
O. Hijab, Finite dimensional causal functionals of Brownian motions in nonlinear stochastic problems, Proceedings of the NATO-ASI on Nonlinear Stochastic Problems, ed. by R. S. Bucy, Reidel(1982).
S. Kusuoka and D. W. Stroock, The partial Malliavin calculus and its Application to nonlinear filtering, Stochastics 12 (1984), 83–142.
P. Malliavin, Stochastic Calculus of Variations and Hypoelliptic Operators, in Proceedings of the International Symposium on Stochastic Differential Equations, ed. by K. Itô, Kinokuniya (1978).Springer-Verlag (1984).
S. I. Marcus, Algebraic and Geometric Methods in Nonlinear Filtering Theory, SIAM J. Control and Optimization 22 (1984), 817–844.
D. Michel, Regularité des lois conditionelles en théorie du filtrage non-lineaire et calcul des variations stochastiques, J. Funct. Anal. 41 (1981), 8–36.
D. Michel and E. Pardoux, An Introduction to Malliavin's Calculus and some of its Applications, to appear in a volume of Lecture Notes in Control and Information Sciences, Springer-Verlag, New York.
S. K. Mitter, Filtering Theory and Quantum Fields, Asterisque 75–76 (1978), 199–206.
D. Ocone, Multiple integral expansions in nonlinear filtering, Stochastics 10 (1983), 1–30.
D. Ocone, Stochastic Calculus of Variations for Stochastic Partial Differential Equations, J. Funct. Anal., to appear.
D. Ocone, Probability distributions for conditional statistics in the cubic sensor problem, Mathematics of Systems, Signals, and Control 1 (1988)
D. Ocone, A guide to the stochastic calculus of variations, to appear in Proceedings of the workshop on Stochastic Differential Systems, Silivri, Turkey, 1986, Lecture Notes in Mathematics, Springer-Verlag.
E. Pardoux, Equations of nonlinear filtering and applications to stochastic control with partial observations, Nonlinear Filtering and Stochastic Control, Lecture Notes in Mathematics 972, 208–248, Springer-Verlag, New York, 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Ocone, D., Pardoux, E. (1989). A Lie algebraic criterion for non-existence of finite dimensionally computable filters. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083947
Download citation
DOI: https://doi.org/10.1007/BFb0083947
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51510-4
Online ISBN: 978-3-540-48200-0
eBook Packages: Springer Book Archive
