A superprocess with a disappearing self-interaction (Q1908215)

The authors consider a system of independent branching Brownian motions, with a weak interaction between the particles, which affects the diffusion but not the branching. The interaction is chosen in such a way that it disappears at the limit when one considers the distribution of the superprocess \(X\). However the authors introduce processes which describe the diffusion part of the branching diffusion processes and prove that they converge in distribution to a process \(W\). Moreover, at the limit, the joint distribution of \((W,X)\) is absolutely continuous with respect to the noninteracting system, and not identical. So, while the pair \((X,W)\) does remember the interaction, it is only at the level of the joint distribution and not at the level of the marginal of the distribution of \(X\). The process \(W\) contains nevertheless useful information and is called by the authors ``ghost process''.