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

In: Itô’s Stochastic Calculus and Probability Theory

Author

Listed:
  • Yasuji Hashimoto

    (Osaka University, Department of Mathematics, Graduate School of Science)

  • Shojiro Manabe

    (Osaka University, Department of Mathematics, Graduate School of Science)

  • Yukio Ogura

    (Saga University, Department of Mathematics)

Abstract

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.

Suggested Citation

  • Yasuji Hashimoto & Shojiro Manabe & Yukio Ogura, 1996. "Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion," Springer Books, in: Nobuyuki Ikeda & Shinzo Watanabe & Masatoshi Fukushima & Hiroshi Kunita (ed.), Itô’s Stochastic Calculus and Probability Theory, pages 129-139, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-68532-6_8
    DOI: 10.1007/978-4-431-68532-6_8
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