摘要
设M是连通Riemann流形,Z是M上C′类向量场,L=(△+Z),本文使用Kendall的耦合分析,给出了参考测度为L-扩散过程在t时刻分布的对数Sobolev常数的估计,并由此建立了轨道空间上的对数Sobolev不等式。此外,本文还给出了流形上的对数Sobolev常数的一个上界估计,所获结果,是对文[1],[2]和[3]的相应结果的推广。
Let (M, g) be a connected Riemannian manifold and let L = 1/2(Δ + Z) for some C1-vector field Z. This paper uses Kendall's coupling analysis to obtain an estimation of the logarithmic Sobolev (abbrev. L.S.) constant with respect to the distribution of the L-diffusion process at time t, which then is used to prove a L. S. inequality on the path space. The main result can be considered as an extension of [1] in which Z is taken to be zero. Moreover, as a generalization to [2; Theorem 1.5] and [3; Theorem 1] which were proved for diffusions on Rd, an upper bound estimation of L.S. constant for the L-diffusion process is also presented.
出处
《应用概率统计》
CSCD
北大核心
1996年第3期255-264,共10页
Chinese Journal of Applied Probability and Statistics
基金
Supported in part by NFSC
the State Education Commission of China
