Limit Theorems. Laws of Large Numbers. Central Limit Theorems

1989 ◽  
pp. 63-69
Author(s):  
T. Cacoullos
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Laws Of Large Numbers ◽  
Large Numbers

Limit theorems for sums of general functions of m-spacings

1984 ◽  
Vol 96 (3) ◽  
pp. 517-532 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Asymptotic Properties ◽  
Central Limit Theorems ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Explicit Formulae ◽  
General Distributions

Laws of large numbers and central limit theorems are proved for sums of general functions of m-spacings from general distributions. Explicit formulae are given for the norming constants. The results enable us to describe asymptotic properties of distributional tests under fixed alternatives. A generalization of Kimball's spacings test is considered in detail.

scholarly journals Limit theorems for multivariate Brownian semistationary processes and feasible results

2019 ◽  
Vol 51 (03) ◽  
pp. 667-716
Author(s):  
Riccardo Passeggeri ◽  
Almut E. D. Veraart
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Laws Of Large Numbers ◽  
Stationary Increments ◽  
Large Numbers ◽  
Weak Laws

AbstractIn this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems, and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.

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