Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.
In this paper,we prove approximations of multifractional Brownian motions with moving-average representations and of those with harmonizable representations in the space of continuous functions on [0,1]. These approximations are constructed by Poisson processes.
In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.
A relationship between continuous state population-size-dependent branching （CSDB） processes with or without immigration and discrete state population-size-dependent branching （DSDB） processes with or without immigration is established via the representation of the former. Based on this relationship, some limiting distributions of CSDB processes with or without immigration are obtained.
We study the functional limits of continuous-time random walks （CTRWs） with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an a-stable Levy process in D（[0, 1]） with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D（[0, 1]） with J1-topology.
