scholarly journals Local Central Limit Theorems in Stochastic Geometry

2011 ◽  
Vol 16 (0) ◽  
pp. 2509-2544
Author(s):  
Mathew Penrose ◽  
Yuval Peres
Keyword(s):  
Central Limit ◽  
Stochastic Geometry ◽  
Limit Theorems ◽  
Central Limit Theorems

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.

scholarly journals Pressure Function and Limit Theorems for Almost Anosov Flows

2021 ◽  
Vol 382 (1) ◽  
pp. 1-47
Author(s):  
Henk Bruin ◽  
Dalia Terhesiu ◽  
Mike Todd
Keyword(s):  
Thermodynamic Properties ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stable Laws ◽  
Analytic Framework ◽  
Pressure Function ◽  
Hyperbolic Flows ◽  
Anosov Flows ◽  
Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

scholarly journals Central limit theorems for supercritical superprocesses

2015 ◽  
Vol 125 (2) ◽  
pp. 428-457 ◽  
Author(s):  
Yan-Xia Ren ◽  
Renming Song ◽  
Rui Zhang
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

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