Laws of large numbers and the central limit theorem for sequences of coefficients of rotational expansions

1997 ◽  
Vol 87 (6) ◽  
pp. 4180-4186
Author(s):  
N. A. Sidorov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Laws Of Large Numbers ◽  
The Central Limit Theorem ◽  
Large Numbers

The Patterns of Large Numbers

2019 ◽  
pp. 43-66
Author(s):  
Steven J. Osterlind
Keyword(s):  
Probability Theory ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
French Revolution ◽  
Central Limit ◽  
Historical Context ◽  
Binomial Theorem ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
First Time

This chapter advances the historical context for quantification by describing the climate of the day—social, cultural, political, and intellectual—as fraught with disquieting influences. Forces leading to the French Revolution were building, and the colonists in America were fighting for secession from England. During this time, three important number theorems came into existence: the binomial theorem, the law of large numbers, and the central limit theorem. Each is described in easy-to-understand language. These are fundamental to how numbers operate in a probability circumstance. Pascal’s triangle is explained as a shortcut solving some binomial expansions, and Jacob Bernoulli’s Ars Conjectandi, which presents the study of measurement “error” for the first time, is discussed. In addition, the central limit theorem is explained in terms of its relevance to probability theory, and its utility today.

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.

The Law of Large Numbers and the Central Limit Theorem

1996 ◽  
pp. 92-96
Author(s):  
Richard L. Scheaffer ◽  
Ann Watkins ◽  
Mrudulla Gnanadesikan ◽  
Jeffrey A. Witmer
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
The Law
Sign in / Sign up

Export Citation Format

Share Document