I understand that in the simple branching process, each object gives birth to its children according to the same distribution. However, I now need to handle a special branching process in which objects generate decedents according to different distributions. For example, objects generate objects according to a Gaussian distribution N(μ,σ)， where μ is decided by the generation of the object. Or, μ might be a function of the life time of the object. Are there existing studies on this kind of branching process, which is an extention of the simple Galton-Watson or Bellman-Harris process? Thank you!