151. Convergence of partial sum processes to stable processes with application for aggregation of branching processes
- Author
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Barczy, Matyas, Nedényi, Fanni K., and Pap, Gyula
- Subjects
Mathematics - Probability ,60G10, 60G52, 60E07, 60J80 - Abstract
We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a strongly stationary sequence to the corresponding finite dimensional distributions of a non-Gaussian stable process instead of weak convergence of the partial sums themselves to a non-Gaussian stable distribution. As an application, we describe the asymptotic behaviour of finite dimensional distributions of aggregation of independent copies of a strongly stationary subcritical Galton--Watson branching process with regularly varying immigration having index in $(0, 1) \cup (1, 4/3)$ in a so-called iterated case, namely when first taking the limit as the time scale and then the number of copies tend to infinity., Comment: 46 pages. In Appendices we recall some notions and statements from arXiv:1906.00373
- Published
- 2019