Skip to main content
Log in

A probabilistic proof and applications of Wiener's test for the heat operator

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Bauer, H.: Heat balls and Fulks measures. Ann. Acad. Sci. Fen. Ser. A.I Math.10, 67–82 (1985)

    Google Scholar 

  2. Doob, J.L.: Classical potential theory and its probabilistic counterpart. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  3. Erdös, P.: On the law of the iterated logarithm. Ann. Math.43, 419–436 (1942)

    Google Scholar 

  4. Evans, L.C., Gariepy, R.F.: Wiener's criterion for the heat equation. Arch. Rat. Mech. Anal.78, 293–314 (1982)

    Google Scholar 

  5. Feller, W.: On the general form of the so called law of iterated logarithm. Trans. Amer. Math. Soc.54, 373–402 (1943)

    Google Scholar 

  6. Feller, W.: An introduction to probability theory and its applications. Vol. II, 2nd. edn. New York Wiley 1971

    Google Scholar 

  7. Fulks, W.: A mean value theorem for the heat equation. Proc. Amer. Math. Soc.17, 6–11 (1966)

    Google Scholar 

  8. Ito, K., McKean Jr., H.P.: Diffusion processes and their sample paths. Berlin Heidelberg New York: Springer 1965

    Google Scholar 

  9. Lamperti, J.: Wiener's test and markov chains. J. Math. Anal. Appl.6, 58–66 (1963)

    Google Scholar 

  10. Lévy, P.: Théorie de l'addition des variables aléatoires. Paris: Gautier-Villars 1937

    Google Scholar 

  11. Motoo, M.: Proof of the law of iterated logarithm through diffusion equation. Ann. Inst. Statis. Math.10, 21–28 (1959)

    Google Scholar 

  12. Petrovskii, I.: Zur ersten Randwertaufgabe der Wärmeleitungsgleichung. Compos. Math.1, 383–419 (1935)

    Google Scholar 

  13. Watson, N.A.: Thermal capacity. Proc. Lond. Math. Soc.37, 342–362 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Uchiyama, K. A probabilistic proof and applications of Wiener's test for the heat operator. Math. Ann. 283, 65–86 (1989). https://doi.org/10.1007/BF01457502

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01457502

Keywords

Navigation