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Stochastic Analysis pp 37–49Cite as

Short time asymptotics for fundamental solutions of diffusion equations

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

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References

  1. D. G. Aronson: Isolated singularities of solutions of second order parabolic equations, Arch. Ration. Mech. Anal., 19(1965), 231–238.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  3. V. S. Buslaev: Continum integrals and the asymptotic behavior of the solution of parabolic equation as t → 0. Application to diffraction, Topics in Math. Phys. 2(1968), ed. by M. Sh. Birman, 67–86.

    Google Scholar 

  4. P. Hsu: Short time asymptotics of the heat kernel on concave boundary, preprint.

    Google Scholar 

  5. N. Ikeda: On the asymptotic behavior of the fundamental solution of the heat equation on certain manifolds, Proc. Taniguchi Intern. Symp. on Stochastic Anal., Katata and Kyoto, 1982, ed. by K. Itô, Kinokuniya/North-Holland, 1984, 169–195.

    Google Scholar 

  6. Y. Kannai: Off diagonal short time asymptotics for fundamental solutions of diffusion equations, Comm. Part. Diffs. Equat., 2(1977), 781–830.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Kusuoka: The generalized Malliavin calculus based on Brownian sheet and Bismut's expansion for large deviation, Lecture Notes in Math., 1158(1986), 141–157.

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Malliavin: Calcul des variations stochastiques subordonné au processus de la chaleur, C. R. Acad. Sc. Paris, Série I, 295(1982), 167–172.

    MathSciNet  MATH  Google Scholar 

  9. P. Malliavin: Implicit functions in finite corank on the Wiener space, Proc. Taniguchi Intern. on Stochastic Analy., Katata and Kyoto, 1982 ed. by K. Itô, Kinokuniya/North-Holland, 1984, 369–386.

    Google Scholar 

  10. R. B. Melrose and M. E. Taylor: Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle, Adv. in Math., 55(1985), 242–315.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Milnor: Morse theory, Annals. Math. Studies, 51, Princeton Univ. Press, 1963.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. S. R. S. Varadhan: On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math., 20(1967), 431–455.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics. Faculty of Science, Osaka University, 560, Toyonaka, Osaka, Japan

    Nobuyuki Ikeda

  2. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Shigeo Kusuoka

Authors
  1. Nobuyuki Ikeda
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  2. Shigeo Kusuoka
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Michel Métivier Shinzo Watanabe

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© 1988 Springer-Verlag

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Ikeda, N., Kusuoka, S. (1988). Short time asymptotics for fundamental solutions of diffusion equations. In: Métivier, M., Watanabe, S. (eds) Stochastic Analysis. Lecture Notes in Mathematics, vol 1322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077865

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  • DOI: https://doi.org/10.1007/BFb0077865

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19352-4

  • Online ISBN: 978-3-540-39232-3

  • eBook Packages: Springer Book Archive

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