Skip to main content

Diffusion processes and heat kernels on certain nilpotent groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1322)

Keywords

  • Vector Field
  • Heat Kernel
  • Heisenberg Group
  • Nilpotent Group
  • Wiener Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • 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. R.Azencott: Diffusions invariantes sur le groupes d'Heisenberg; une étude de cas d'après B.Gaveau, Géodésiques et diffusions en temps petit, Astérisque 84–85 (1981), 227–235.

    Google Scholar 

  2. R. Azencott: Densités des diffusions en temps petit: développements asymptotiques. Séminaire de Prob. XVIII, 1982/1983 Lecture Note in Math. 1059, Springer (1984), 402–498.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. G.Ben Arous: Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus, preprint.

    Google Scholar 

  4. J.-M. Bismut: Large deviations and the Malliavin calculus, Progress in Math. 45, Birkhäuser, 1984.

    Google Scholar 

  5. B. Gaveau: Principe de moindre action, propagation de la chaleur, estimeés sous elliptiques sur certains groupes nilpotents Acta Math. 139 (1977), 95–153.

    MathSciNet  Google Scholar 

  6. I.M.Gelfand and G.E.Silov: Generalized functions, Vol.1, Academic Press, 1964.

    Google Scholar 

  7. S. Kusuoka and D.W. Stroock: Applications of the Malliavin calculus, Part III J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34(1987), 391–442.

    MathSciNet  MATH  Google Scholar 

  8. R. Léandre: Intégration dans la fibre associée à une diffusion dégénérée, Probab. Th. Rel. Fields 76 (1987), 341–358

    CrossRef  MATH  Google Scholar 

  9. S.A. Molchanov: Diffusion processes and Riemannian geometry, Russian Math. Surveys 30 (1975), 1–63.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. S.Takanobu: Diagonal short time asymptotics of heat kernels for certain degenerate second order differential operators of Hörmander type, to appear in Publ. RIMS, Kyoto Univ..

    Google Scholar 

  11. H. Uemura: On a short time expansion of the fundamental solution of heat equations by the method of Wiener functionals, J. Math. Kyoto Univ. 27 (1987), 417–431.

    MathSciNet  MATH  Google Scholar 

  12. S. Watanabe: Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, The Annals of Probab. 15 (1987), 1–39.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Uemura, H., Watanabe, S. (1988). Diffusion processes and heat kernels on certain nilpotent groups. In: Métivier, M., Watanabe, S. (eds) Stochastic Analysis. Lecture Notes in Mathematics, vol 1322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077875

Download citation

  • DOI: https://doi.org/10.1007/BFb0077875

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19352-4

  • Online ISBN: 978-3-540-39232-3

  • eBook Packages: Springer Book Archive