Skip to main content
SpringerLink
Log in

A Markov property for Gaussian processes with a multidimensional parameter

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

References

  1. Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton: Von Nostrand 1965.

    Google Scholar 

  2. Aronszajn, N., Theory of reproducing kernels. Trans. Amer. Math. Soc. 68, 337–404 (1950).

    Google Scholar 

  3. Dolph, C. L., & M. A. Woodbury, On the relation between Green's functions and covariances of certain stochastic processes and its application to unbiased linear prediction. Trans. Amer. Math. Soc. 72, 519–550 (1952).

    Google Scholar 

  4. Doob, J. L., The elementary Gaussian processes. Annals. of Math. Stat. 15, 229–282 (1944).

    Google Scholar 

  5. Hida, T., Canonical representations of Gaussian processes and their applications. Mem. Coll Sci., U. of Kyoto, ser. A, Math. 33, 109–155 (1960).

    Google Scholar 

  6. Hunt, G. A., Martingales et Processus de Markov. Paris: Dunod 1966.

    Google Scholar 

  7. Levinson, N., & H. P., McKean Jr., Weighted Trigonometrical approximation on R1 with application to the germ field of a stationary Gaussian noise. Acta Math. 112, 99–143 (1964).

    Google Scholar 

  8. McKean, H. P., Jr., Brownian motion with a several dimensional time. Theory Prob. Applications 8, 335–354 (1963).

    Google Scholar 

  9. Molchan, G. M., On some problems concerning Brownian motion in Lévy's sense. Theory Prob. Applications 12, 682–690 (1967).

    Google Scholar 

  10. Peetre, J., Rectification a l'article ≪Une caractérisation abstraite des opérateurs différentiels≫. Math. Scand. 8, 116–120 (1960).

    Google Scholar 

  11. Pitt, L., Some problems in the spectral theory of stationary processes on R n (to appear).

  12. Sirao, T., On the continuity of Brownian motion with a multidimensional parameter. Nagoya Math. Jour. 16, 135–156 (1960).

    Google Scholar 

  13. Sobolev, S. L., Applications of Functional Analysis in Mathematical Physics. [Trans. from the Russian by F. E. Browder]. Amer. Math. Soc. Providence (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22901, Charlottesville

    Loren D. Pitt

Authors
  1. Loren D. Pitt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by M. Kac

This research was partially supported by Army Research Office Grant ARO-D-1005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pitt, L.D. A Markov property for Gaussian processes with a multidimensional parameter. Arch. Rational Mech. Anal. 43, 367–391 (1971). https://doi.org/10.1007/BF00252003

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00252003

Keywords

Search

Navigation