Central Limit Theorems for Additive Tree Parameters with Small Toll Functions

2014 ◽  
Vol 24 (1) ◽  
pp. 329-353 ◽  
Author(s):  
STEPHAN WAGNER
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Normal Limit ◽  
Central Limit Theorems ◽  
Limit Laws ◽  
Polya Trees ◽  
Additive Tree ◽  
Log Normal ◽  
Recursive Trees ◽  
Parameter Values

We call a tree parameter additive if it can be determined recursively as the sum of the parameter values of all branches, plus a certain toll function. In this paper, we prove central limit theorems for very general toll functions, provided that they are bounded and small on average. Simply generated families of trees are considered as well as Pólya trees, recursive trees and binary search trees, and the results are illustrated by several examples of parameters for which we prove normal or log-normal limit laws.

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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