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In this paper we study the convergence in distribution and the local limit theorem for the partial sums of linear random fields with i.i.d. innovations that have infinite second moment and belong to the domain of attraction of a stable law with index $0<alphaleq2$ under the condition that the innovations are centered if $1<alphaleq2$ and are symmetric if $alpha=1$. We establish these two types of limit theorems as long as the linear random fields are well-defined, the coefficients are either absolutely summable or not absolutely summable.
We consider a critical superprocess ${X;mathbf P_mu}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index $gamma_0 > 1$. We first show that, under some conditions, $mathbf P_{mu}(|X_t| eq 0)$ conver
Let $r=r(n)$ be a sequence of integers such that $rleq n$ and let $X_1,ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $mathbb{R}^n$. Limit theorems for the log-volume and t
There have been several recent articles studying homology of various types of random simplicial complexes. Several theorems have concerned thresholds for vanishing of homology, and in some cases expectations of the Betti numbers. However little seems
Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural disasters, mea
In this paper, we study the asymptotic behavior of a supercritical $(xi,psi)$-superprocess $(X_t)_{tgeq 0}$ whose underlying spatial motion $xi$ is an Ornstein-Uhlenbeck process on $mathbb R^d$ with generator $L = frac{1}{2}sigma^2Delta - b x cdot a