Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion
Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion
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奇异扩散热核的短时渐近和近似
DOI：
10.1007/978-4-431-68532-6_8
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Y. Ogura
中科院分区：
文献类型：
--
作者：
Yasuji Hashimoto;Shojiro Manabe;Y. Ogura
扩散过程的类是如此广泛，它不仅包括与具有可测系数的椭圆算子相关的过程，而且还包括与具有分布系数的生成元相关的过程，如测度甚至测度的导数。而一维问题的解在20世纪50、60年代由W。Feller，K.伊藤，H. P. McKean和E.B. Dynkin，其中。然而，多层面的情况则大不相同，问题仍然悬而未决。
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.