scholarly journals Moments and Central Limit Theorems for Some Multivariate Poisson Functionals

2014 ◽  
Vol 46 (2) ◽  
pp. 348-364 ◽  
Author(s):  
Günter Last ◽  
Mathew D. Penrose ◽  
Matthias Schulte ◽  
Christoph Thäle
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Central Limit ◽  
Malliavin Calculus ◽  
Limit Theorems ◽  
Measurable Space ◽  
Central Limit Theorems ◽  
Poisson Processes ◽  
Chaos Expansion

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-Itô integrals with respect to the compensated Poisson process. Also, we present a multivariate central limit theorem for a vector whose components admit a finite chaos expansion of the type of a Poisson U-statistic. The approach is based on recent results of Peccati et al. (2010), combining Malliavin calculus and Stein's method; it also yields Berry-Esseen-type bounds. As applications, we discuss moment formulae and central limit theorems for general geometric functionals of intersection processes associated with a stationary Poisson process of k-dimensional flats in .

scholarly journals Moments and Central Limit Theorems for Some Multivariate Poisson Functionals

2014 ◽  
Vol 46 (02) ◽  
pp. 348-364 ◽  
Author(s):  
Günter Last ◽  
Mathew D. Penrose ◽  
Matthias Schulte ◽  
Christoph Thäle
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Central Limit ◽  
Malliavin Calculus ◽  
Limit Theorems ◽  
Measurable Space ◽  
Central Limit Theorems ◽  
Poisson Processes ◽  
Chaos Expansion

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-Itô integrals with respect to the compensated Poisson process. Also, we present a multivariate central limit theorem for a vector whose components admit a finite chaos expansion of the type of a PoissonU-statistic. The approach is based on recent results of Peccatiet al.(2010), combining Malliavin calculus and Stein's method; it also yields Berry-Esseen-type bounds. As applications, we discuss moment formulae and central limit theorems for general geometric functionals of intersection processes associated with a stationary Poisson process ofk-dimensional flats in.

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
Sign in / Sign up

Export Citation Format

Share Document