Limit theorem for the spread of branching process with stabilizing drift

We consider two models of branching processes. The first model is a branching diffusion which underlying motion has a stabilizing drift and a continuous perturbation governed by a standard Brownian motion. The second model is a similar branching process but with the random term of the movement of an individual particle described by a time homogeneous process with independent jump increments. Our aim is to find an asymptotic behavior for large time t of the right frontier of the branching process over the time interval [0, t]. A generalization to a multi-dimensional case for the branching diffusion is also presented