On States of Total Weighted Occupation Times for Superdiffusions  

作　　者：REN Yan Xia Center for Advanced Study. Tsinghua University. Beijing 100084. P. R. China 

出　　处：《Acta Mathematica Sinica,English Series》2002年第1期69-78,共10页数学学报（英文版）

基　　金：This work is supported by NNSF of China(Grant No. 19801019);China Postdoctoral Foundation

摘　　要：Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D) has absolutey continuous states. And for particular ψ(z) = z^(l+, 0<B ≤1. we prove that. in the case d<2 + 2/B. Y_^(D) is absolutely continuous with respect to the Lebesgue measure in D. whereas in the case d>2 + 2/B. it is singular. As we know the absolute continuity and singularity of Y_(D have not been discussed before.Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D) has absolutey continuous states. And for particular ψ(z) = z^(l+, 0<B ≤1. we prove that. in the case d<2 + 2/B. Y_^(D) is absolutely continuous with respect to the Lebesgue measure in D. whereas in the case d>2 + 2/B. it is singular. As we know the absolute continuity and singularity of Y_(D have not been discussed before.

关 键 词：Total weighted occupation time SUPERDIFFUSION Absolutely continuous state Singular states 

分 类 号：O175[理学—数学]