带交互作用测度值分枝过程的绝对连续性(英文)

Absolute Continuity of Measure Branching Processes with Interaction

本文研究Meleard-Roelly（1992，1993）和Metivier（1987）构造的带交互作用的测度值分枝过程的状态性质．我们证明在自然假设下该过程关于Lebesgue测度是绝对连续的，其密度有连续修正且满足一个随机偏微分方程．

We study the state properties of the measure branchiug process over IR with mean field interaction coustructed by Meleard and Roelly (1992, 1993) and Metivier (1987). It is proved that, under natural hypotheses, the process is absolutely continuous with respect to the Lebesgue measure and the density process has a continuous version which satisfies a stochastic partial differential equation.