Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion

  • Yasuji Hashimoto
  • Shojiro Manabe
  • Yukio Ogura


The class of diffusion processes is so wide that it includes not only the processes associated with elliptic operators with measurable coefficients but also those associated with the generators with distribution coefficients like measures or even derivatives of measures. That of one-dimensional ones is completely determined in 1950’s and 1960’s by many authors such as W. Feller, K. Itô, H. P. McKean and E.B. Dynkin, among others. The situation for multidimensional ones is however quite different and the problem is still open.


Distance Function Heat Kernel Dominate Convergence Theorem Dirichlet Form Symmetric Form 
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Copyright information

© Springer-Verlag Tokyo 1996

Authors and Affiliations

  • Yasuji Hashimoto
    • 1
  • Shojiro Manabe
    • 1
  • Yukio Ogura
    • 2
  1. 1.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonaka, Osaka 560Japan
  2. 2.Department of MathematicsSaga UniversitySaga 840Japan

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