Regularity of the Density for the Total Weighted Occupation Measure of Super-Brownain Motion  

作　　者：Rong Li LIU 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第8期1557-1572,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant Nos. 10871103 and 10971003）

摘　　要：Let （Xt） be a super-Brownian motion in a bounded domain D in R^d. The random measure Y^D（.） = ∫o^∞ Xt（.）dt is called the total weighted occupation time of （Xt）. We consider the regularity properties for the densities of a class of yD. When d = 1, the densities have continuous modifications. When d ≥ 2, the densities are locally unbounded on any open subset of D with positive y D （dx）-measure.Let （Xt） be a super-Brownian motion in a bounded domain D in R^d. The random measure Y^D（.） = ∫o^∞ Xt（.）dt is called the total weighted occupation time of （Xt）. We consider the regularity properties for the densities of a class of yD. When d = 1, the densities have continuous modifications. When d ≥ 2, the densities are locally unbounded on any open subset of D with positive y D （dx）-measure.

关 键 词：SUPERPROCESSES Poisson point processes REGULARITY total weighted occupation time 

分 类 号：O178[理学—数学] S823.4[理学—基础数学]