Stable central limit theorems for super ornstein-uhlenbeck processes

Yan Xia Ren, Renming Song, Zhenyao Sun, Jianjie Zhao

科研成果: 期刊稿件文章同行评审

5 引用 (Scopus)

摘要

In this paper, we study the asymptotic behavior of a supercritical (ξ, ψ)-superprocess (Xt)t≥0 whose underlying spatial motion ξ is an Ornstein-Uhlenbeck process on Rd with generator L =12σ2 ∆ − bx · ∇ where σ, b > 0; and whose branching mechanism ψ satisfies Grey’s condition and a perturbation condition which guarantees that, when z → 0, ψ(z) = −αz + ηz1+β (1 + o(1)) with α > 0, η > 0 and β ∈ (0, 1). Some law of large numbers and (1 + β)-stable central limit theorems are established for (Xt(f))t≥0, where the function f is assumed to be of polynomial growth. A phase transition arises for the central limit theorems in the sense that the forms of the central limit theorem are different in three different regimes corresponding to the branching rate being relatively small, large or critical at a balanced value.

源语言英语
文章编号141
期刊Electronic Journal of Probability
24
DOI
出版状态已出版 - 2019
已对外发布

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