Linear maps on the space of all bounded observables preserving maximal deviation

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.Comment: 27 pages. To appear in J. Funct. Ana

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