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)...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.展开更多
基金This work is supported by NNSF of China(Grant No. 19801019)China Postdoctoral Foundation
文摘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.
