scholarly journals Stable limit theorems on the Poisson space

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Ronan Herry
Keyword(s):  
Limit Theorems ◽  
Stable Limit ◽  
Poisson Space

Some Functional Stable Limit Theorems

1973 ◽  
Vol 16 (2) ◽  
pp. 173-177 ◽  
Author(s):  
D. R. Beuerman
Keyword(s):  
Weak Convergence ◽  
Limit Theorems ◽  
Stable Process ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Stable Limit ◽  
Stable Law ◽  
Partial Sum Process ◽  
Image Position

Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,1whereandwhere L(n) is a function of slow variation; also take S0=0, B0=l.In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.

scholarly journals α-Stable limit theorems for sums of dependent random vectors

1989 ◽  
Vol 29 (2) ◽  
pp. 219-251 ◽  
Author(s):  
Adam Jakubowski ◽  
Maria Kobus
Keyword(s):  
Limit Theorems ◽  
Stable Limit ◽  
Random Vectors

scholarly journals Stable limit theorems for empirical processes under conditional neighborhood dependence

Bernoulli ◽  
2019 ◽  
Vol 25 (2) ◽  
pp. 1189-1224 ◽  
Author(s):  
Ji Hyung Lee ◽  
Kyungchul Song
Keyword(s):  
Limit Theorems ◽  
Empirical Processes ◽  
Stable Limit

A new ideal metric with applications to multivariate stable limit theorems

1992 ◽  
Vol 94 (2) ◽  
pp. 163-187 ◽  
Author(s):  
S. T. Rachev ◽  
L. R�schendorf
Keyword(s):  
Limit Theorems ◽  
Stable Limit

scholarly journals Almost sure central limit theorems in stochastic geometry

2020 ◽  
Vol 52 (3) ◽  
pp. 705-734
Author(s):  
Giovanni Luca Torrisi ◽  
Emilio Leonardi
Keyword(s):  
Central Limit ◽  
Stochastic Geometry ◽  
Limit Theorems ◽  
Voronoi Tessellation ◽  
Edge Length ◽  
Central Limit Theorems ◽  
Geometric Graphs ◽  
Random Geometric Graphs ◽  
Poisson Space ◽  
Set Approximation

AbstractWe prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising in stochastic geometry. As a consequence, we provide almost sure central limit theorems for (i) the total edge length of the k-nearest neighbors random graph, (ii) the clique count in random geometric graphs, and (iii) the volume of the set approximation via the Poisson–Voronoi tessellation.

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