Smoothness of the intensity measure density for interacting branching diffusions with immigra\-tions (Q1888356)

Consider a sub-critical branching diffusion on \(\mathbb{R}^n\) with constant branching density, a local space-dependent offspring law, and interaction via population-dependent diffusion coefficients. Let there be immigration at a constant rate, the immigrating particle distributed according to some fixed measure. Using Malliavin calculus it is shown that the intensity measure of the invariant measure of the process has a density which is continuous and possesses first order partial derivatives. The density is bounded if the immigration measure is absolutely continuous.