Limit theorems for geometric functionals of Gibbs point processes
نویسندگان
چکیده
منابع مشابه
Limit theorems for geometric functionals of Gibbs point processes
Observations are made on a point process Ξ in R in a window Qλ of volume λ. The observation, or ‘score’ at a point x, here denoted ξ(x, Ξ), is a function of the points within a random distance of x. When the input Ξ is a Poisson or binomial point process, the large λ limit theory for the total score ∑ x∈Ξ∩Qλ ξ(x, Ξ ∩Qλ), when properly scaled and centered, is well understood. In this paper we es...
متن کاملStabilization and limit theorems for geometric functionals of Gibbs point processes
Given a Gibbs point process P on R having a weak enough potential Ψ, we consider the random measures μλ := P x∈P∩Qλ ξ(x,P ∩Qλ)δx/λ1/d , where Qλ := [−λ /2, λ/2] is the volume λ cube and where ξ(·, ·) is a translation invariant stabilizing functional. Subject to Ψ satisfying a localization property and translation invariance, we establish weak laws of large numbers for λ−1μλ(f), f a bounded test...
متن کاملLimit Theorems for Empirical Processes of Cluster Functionals
Let (Xn,i)1≤i≤n,n∈N be a triangular array of row-wise stationary R-valued random variables. We use a “blocks method” to define clusters of extreme values: the rows of (Xn,i) are divided into mn blocks (Yn,j), and if a block contains at least one extreme value the block is considered to contain a cluster. The cluster starts at the first extreme value in the block and ends at the last one. The ma...
متن کاملLimit Theorems for Multifractal Products of Geometric Stationary Processes
Abstract: We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck processes driven by Lévy motion and their finite and infinite superpositions. We present the general conditions for the Lq convergence of cumulative processes to the limiting processes and investigate their q-th order moments and R...
متن کاملLocal Limit Theorems for Gibbs{markov Maps
We prove conditional local limit theorems for Gibbs-Markov processes whose marginals are in the domain of attraction of a stable law with order in (0;2). c 1996.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2013
ISSN: 0246-0203
DOI: 10.1214/12-aihp500