Abstract
Let the signal be defined by dxt = m(xt)dt + σ(xt)dwt and observed via dyt = h(xt)dt + dνt where w and ν are independent Brownian motions. The filtering problem is the problem of determining the conditional distribution of xt conditioned on yθ, 0 ≤ Θ ≤ t and a basic question is that of existence of finite dimensional filters, i.e., when can the filtering problem be solved by a set of finite dimensional stochastic differential equations driven by the observation yt. Following the results on the nonexistence of finite dimensional filters, the question arises whether there exists a set of finite dimensional equations driven by yt which determines the conditional moment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 D. Reidel Publishing Company
About this paper
Cite this paper
Zakai, M. (1981). A Footnote to the Papers which Prove the Nonexistence of Finite Dimensional Filters. In: Hazewinkel, M., Willems, J.C. (eds) Stochastic Systems: The Mathematics of Filtering and Identification and Applications. NATO Advanced Study Institutes Series, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8546-9_37
Download citation
DOI: https://doi.org/10.1007/978-94-009-8546-9_37
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-8548-3
Online ISBN: 978-94-009-8546-9
eBook Packages: Springer Book Archive