Skip to main content

On a Markovian property of Gaussian processes

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 330))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Kawai: On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo Sect. IA 17 (1971), 467–517.

    MathSciNet  MATH  Google Scholar 

  3. H. Komatsu: On ultra-distributions, Katada Symposium, 1971, to appear in Lecture notes in Math., Springer-Verlag.

    Google Scholar 

  4. S. Kotani and Y. Okabe: On a Markovian property of stationary Gaussian process with a multi-dimensional parameter, Katada Symposium, 1971, to appear in Lecture notes in Math., Springer-Verlag.

    Google Scholar 

  5. S. Kotani: On a Markovian property of stationary Gaussian processes with a multi-dimensional parameter, II, Proceedings of the Second Japan-USSR Symposium on Probability Theory.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. H. P. McKean, Jr.: Brownian motion with a several dimensional time, Theor. Probability Appl. 8 (1963), 357–378.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. M. Molchan: On some problems concerning Brownian motion in Lévy's sense, Theor. Probability Appl. 12 (1967), 682–690.

    Article  MATH  Google Scholar 

  9. G. M. Molchan: Characterization of Gaussian fields with Markov property, Dokl. Akad. Nauk USSR 197 (1971), 784–787. (in Russian).

    MathSciNet  Google Scholar 

  10. Y. Okabe: Stationary Gaussian processes with Markovian property and M. Sato's hyperfunctions, to appear in J. Math. Soc. Japan.

    Google Scholar 

  11. L. D. Pitt: A Markov property for Gaussian processes with a multidimensional parameter, Arch. Rational Mech. Anal. 43 (1971), 367–395.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Sato: Theory of hyperfunctions I, II, J. Fac. Sci. Univ. Tokyo Sect. I. 8 (1959), 139–193, 387–437.

    MathSciNet  MATH  Google Scholar 

  13. K. Urbanik: Generalized stationary processes of Markovian character, Studia Math. 21 (1962), 261–282.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

G. Maruyama Yu. V. Prokhorov

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Okabe, Y. (1973). On a Markovian property of Gaussian processes. In: Maruyama, G., Prokhorov, Y.V. (eds) Proceedings of the Second Japan-USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061500

Download citation

  • DOI: https://doi.org/10.1007/BFb0061500

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06358-2

  • Online ISBN: 978-3-540-46956-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics