On convergence properties of infinitesimal generators of scaled multi-type CBI processes

It is a common method for proving weak convergence of a sequence of time-homogeneous Markov processes towards a time-homogeneous Markov process first to show convergence of the corresponding infinitesimal generators and then to check some additional conditions. The aim of the present paper is to investigate convergence properties of discrete infinitesimal generators of appropriately scaled random step functions formed from a multi-type continuous state and continuous time branching process with immigration. We also present a convergence result for usual infinitesimal generators of the branching processes in question appropriately normalized.Comment: 17 pages. Title is changed, and new parts (e.g., Corollary 3.5 and Remark 3.6) are added. In Section 2 we recall some notions and statements from arXiv:1403.0245 and arXiv:1404.224

Statistical inference for critical continuous state and continuous time branching processes with immigration

We study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.Comment: 26 pages. In Section 2 and in Appendices we recall some notions and statements from arXiv:1403.0245 and arXiv:1404.2242. arXiv admin note: substantial text overlap with arXiv:1406.332

Moment formulas for multitype continuous state and continuous time branching processes with immigration

Recursions for moments of multitype continuous state and continuous time branching process with immigration are derived. It turns out that the kth (mixed) moments and the kth (mixed) central moments are polynomials of the initial value of the process, and their degree is at most k and ⌊k/2⌋, respectively