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

Yasuji Hashimoto, Shojiro Manabe and Yukio Ogura
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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

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 129-139 from Springer

Abstract: 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.

Keywords: Distance Function; Heat Kernel; Dominate Convergence Theorem; Dirichlet Form; Symmetric Form (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-4-431-68532-6_8

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