Abstract
One of Professor Norbert Wiener’s beloved projects in his later years was to develop a theory of nonlinear prediction. It was Professor Kiyosi Itô’s discovery of stochastic calculus (now subsumed under the more inclusive title of stochastic analysis) that made such a development possible. This is not the place to describe in detail Professor Itô’s continuing contributions to the subject he helped to create. However, one incident which illustrates his eagerness to explore and assimilate new ideas stands out in my mind.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bhatt, A.G., Karandikar, R.L., (1995): Evolution equations for Markov processes: Applications to the white noise theory of filtering, Applied Mathematics and Optimization 31, 326–348
Bhatt, A.G., Kallianpur, G., Karandikar, R.L. (1995): Uniqueness and robustness of solution of measure valued equations of nonlinear filtering, to appear in Annals of Probability
Budhiraja, A., Kallianpur, G. (1995): Approximations to the solution of the Zakai equations using multiple Wiener and Stratonovich integral expansions, University of North Carolina Center for Stochastic Processes Technical Report No. 447, January 1995. To appear in Stochastics and Stochastic Reports
Budhiraja, A., Kallianpur, G. (1995): Two results on multiple Stratonovich integrals, University of North Carolina Center for Stochastic Processes Technical Report No. 457, June 95. Submitted for publication
Budhiraja, A. and Kallianpur, G. (1995): The Feynman-Stratonovich semigroup and Stratonovich integral expansions in nonlinear filtering, University of North Carolina Center for Stochastic Processes Technical Report No. 466, July 1995. Submitted for publication
Itô, K. (1974): Stochastic differentials, Applied Mathematics and Optimization, 1, 374–380
Itô, K. (1974): Stochastic parallel transport, Probabilistic Methods in Stochastic Differential Equations, Lecture Notes in Mathematics 451, Springer-Verlag, 1–7
Itô, K. (1984): Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces, CBMS Notes, Baton Rouge (1983), SIAM
Johnson, G.W., Kallianpur, G. (1993): Homogeneous chaos, p-forms, scaling and the Feynman integral, Transactions of the American Mathematical Society 340, 503–548
Kallianpur, G., Karandikar, R.L. (1988): White noise theory of prediction, filtering and smoothing, Gordon and Breach, New York
Kunita, H. (1981): Stochastic partial differential equations connected with nonlinear filtering, Nonlinear Filtering and Stochastic Control, Proceedings, Cortona 1981, Lecture Notes in Mathematics 972
Lototsky, S., Mikulevicius, R., Rozovskii, B.L. (1995): Nonlinear Filtering Revisited: A Spectral Approach, CAMS Report 95–3
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Tokyo
About this chapter
Cite this chapter
Kallianpur, G. (1996). Some recent developments in nonlinear filtering theory. In: Ikeda, N., Watanabe, S., Fukushima, M., Kunita, H. (eds) Itô’s Stochastic Calculus and Probability Theory. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68532-6_10
Download citation
DOI: https://doi.org/10.1007/978-4-431-68532-6_10
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-68534-0
Online ISBN: 978-4-431-68532-6
eBook Packages: Springer Book Archive