Titlebook: Stochastic Geometry, Spatial Statistics and Random Fields; Asymptotic Methods Evgeny Spodarev Book 2013 Springer-Verlag Berlin Heidelberg 2

ineffectual

Random Tessellations and Cox Processes,eral classes of Poisson-type tessellations which can describe for example the infrastructure of telecommunication networks, whereas the Cox processes on their edges can describe the locations of network components. An important quantity associated with stationary point processes is their typical Vor

模范

小淡水鱼

构想

Limit Theorems in Discrete Stochastic Geometry,ith the general representation ., where . is finite and where the interactions of . with respect to ., given by ., are spatially correlated. We focus on subadditive methods and stabilization methods as a way to obtain weak laws of large numbers, variance asymptotics, and central limit theorems for n

有权

Introduction to Random Fields,ds (Gaussian, stable, infinitely divisible, Markov and Gibbs fields, etc.) are considered. Correlation theory of stationary random functions as well as elementary nonparametric statistics and an overview of simulation techniques are discussed in more detail.

acquisition

Central Limit Theorems for Weakly Dependent Random Fields,ations are introduced. Then, moment inequalities for sums of dependent random variables are stated which yield e.g. the asymptotic behaviour of the variance of these sums which is essential for the proof of limit theorems. Finally, central limit theorems for dependent random fields are given. Applic

olfction

llibretto

随意

Foundations of Stochastic Geometry and Theory of Random Sets,d measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

只有

Asymptotic Methods for Random Tessellations,cular situation where the inradius of the typical cell is large. We start with precise distributional properties of the circumscribed radius that we use afterwards to provide quantitative information about the closeness of the cell to a ball. We conclude with limit theorems for the number of hyperfaces when the inradius goes to infinity.