Branching processes, integer-valued autoregressions, and non-negative diffusions

2007. október 4. csütörtök 16:15

In the talk I will consider critical branching processes with immigration and integer-valued autoregressive (INAR) processes. The latter one is a special kind of branching processes where the offspings have Bernoulli distribution. I prove a functional limit theorem both for one and multitype case. The limit process is a non-negative diffusion process, the so-called square-root process. The asymptotic behaviour of the conditional least square estimator of the offspring mean is also studied. Finally, inhomogeneous INAR models are investigated.