The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the sur...The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the surface area on ?D if $d< \frac{2}{{a - 1}}$ whereas in the case $d > 1 + \frac{2}{{a - 1}}$ they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1.展开更多
文摘The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the surface area on ?D if $d< \frac{2}{{a - 1}}$ whereas in the case $d > 1 + \frac{2}{{a - 1}}$ they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1.
