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