This paper is a continuation of our recent paper(Electron.J.Probab.,24(141),(2019))and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes(X_(t))t≥0 with branching mec...This paper is a continuation of our recent paper(Electron.J.Probab.,24(141),(2019))and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes(X_(t))t≥0 with branching mechanisms of infinite second moments.In the aforementioned paper,we proved stable central limit theorems for X_(t)(f)for some functions f of polynomial growth in three different regimes.However,we were not able to prove central limit theorems for X_(t)(f)for all functions f of polynomial growth.In this note,we show that the limiting stable random variables in the three different regimes are independent,and as a consequence,we get stable central limit theorems for X_(t)(f)for all functions f of polynomial growth.展开更多
The global supports of super-Poisson processes and super-random walks with a branching mechanism ψ（z）=z^2 and constant branching rate are known to be noncompact. It turns out that, for any spatially dependent branc...The global supports of super-Poisson processes and super-random walks with a branching mechanism ψ（z）=z^2 and constant branching rate are known to be noncompact. It turns out that, for any spatially dependent branching rate, this property remains true. However, the asymptotic extinction property for these two kinds of superprocesses depends on the decay rate of the branching-rate function at infinity.展开更多
基金supported in part by NSFC(Grant Nos.11731009 and 12071011)the National Key R&D Program of China(Grant No.2020YFA0712900)supported in part by Simons Foundation(#429343,Renming Song)。
文摘This paper is a continuation of our recent paper(Electron.J.Probab.,24(141),(2019))and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes(X_(t))t≥0 with branching mechanisms of infinite second moments.In the aforementioned paper,we proved stable central limit theorems for X_(t)(f)for some functions f of polynomial growth in three different regimes.However,we were not able to prove central limit theorems for X_(t)(f)for all functions f of polynomial growth.In this note,we show that the limiting stable random variables in the three different regimes are independent,and as a consequence,we get stable central limit theorems for X_(t)(f)for all functions f of polynomial growth.
基金NNSF of China (Grant No.10471003)Foundation for Authors Awarded Excellent Ph.D.Dissertation
文摘The global supports of super-Poisson processes and super-random walks with a branching mechanism ψ（z）=z^2 and constant branching rate are known to be noncompact. It turns out that, for any spatially dependent branching rate, this property remains true. However, the asymptotic extinction property for these two kinds of superprocesses depends on the decay rate of the branching-rate function at infinity.
