Skip to main content
SpringerLink
Log in

Filtering on manifolds

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

We coasider a partially observable diffusion process (x t,yt)t⩾0 whose unobservable componentx t lives on a submanifold M ofR n. We present some general conditions under which the conditional law ofx t, given the observationsy s ,s ∈ [0,t], admits a density w.r.t. a given measure on M. We characterize the analytical properties of this density by using appropriate Sobolev spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Davis, M. H. A.: Pathwise nonlinear filtering with observations on manifolds, inProc. 25th IEEE Conference on Decision and Control, Athens, 1986, pp. 1337–1338.

  2. Duncan, T. E.: Some filtering results in Riemannian manifolds,Inform. Control 35 (1977), 182–195.

    Google Scholar 

  3. Gyöngy, I. and Krylov, N. V.: On stochastic partial differential equations with unbounded coefficients,Potential Anal. 1 (1992), 233–256.

    Google Scholar 

  4. Gyöngy, I.: Stochastic partial differential equations on manifolds, I,Potential Anal. 2 (1993), 101–113.

    Google Scholar 

  5. Krylov, N. V. and Rozovskii, B. L.: Itô equations in Banach spaces,Itogi Nauki, Teor. Verojatn. 14 (1979), 72–147 (in Russian).

    Google Scholar 

  6. Pardoux, E.: Équations aux dérivées partielles stochastiques non linéaries monotones. Etude des solutions forte de type Itô, Thèse, Université de Paris Sud, Orsay (1975).

    Google Scholar 

  7. Pontier, M. and Szpirglas, J.: Filtrage non-linéaire avec observation sur une varieté,Stochastics 15 (1985), 121–148.

    Google Scholar 

  8. Pardoux, E.: Filtrage non lineéaire et equations aux derivées partielles stochastiques associées, École d'été de Probabilités de Saint-Fleur, 1989.

  9. Rozovskii, B. L.:Stochastic Evolution Systems, Kluwer Academic Publ., Dordrecht, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Probability Theory and Statistics, Eötvös Loránd University, Múzeum krt. 6-8, H-1088, Budapest, Hungary

    István Gyöngy

Authors
  1. István Gyöngy
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by the Hungarian National Foundation of Scientific Research No. 2290.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gyöngy, I. Filtering on manifolds. Acta Appl Math 35, 165–177 (1994). https://doi.org/10.1007/BF00994916

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00994916

Mathematics subject classifications (1991)

Key words

Search

Navigation