Limit Laws for Sums of Independent Random Variables

E379000

mathematical work monograph

Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.

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All labels observed (4)

Label	Occurrences
Limit Laws for Sums of Independent Random Variables canonical	1
Random Variables and Probability Distributions	1
Théorie de l’addition des variables aléatoires	1
limit theorems in probability	1

Statements (35)

Predicate	Object
instanceOf	mathematical work ⓘ monograph ⓘ
assumesKnowledgeOf	measure-theoretic probability ⓘ real analysis ⓘ
audience	graduate students in probability ⓘ researchers in probability theory ⓘ
contribution	clarifies conditions for central limit behavior ⓘ clarifies conditions for law of large numbers ⓘ provides a unified framework for limit laws of sums ⓘ
field	mathematical statistics ⓘ probability theory ⓘ
focus	rigorous treatment of sums of independent random variables ⓘ systematic development of probability limit theorems ⓘ
importance	foundational in the theory of probability limit theorems ⓘ used as a reference in advanced probability courses ⓘ
relatedTo	central limit theorem ⓘ surface form: classical central limit theorem classical law of large numbers ⓘ modern probability textbooks on limit theorems ⓘ
structure	organized around asymptotic results for sums ⓘ
topic	almost sure convergence ⓘ asymptotic behavior of sums ⓘ central limit behavior ⓘ central limit theorem ⓘ convergence in distribution ⓘ convergence in probability ⓘ independent random variables ⓘ law of large numbers ⓘ limit theorems ⓘ normal approximation ⓘ probability limit theorems ⓘ stability of sums ⓘ strong law of large numbers ⓘ sums of independent random variables ⓘ triangular arrays of random variables ⓘ law of large numbers ⓘ surface form: weak law of large numbers

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Aleksandr Khinchin → notableWork → Limit Laws for Sums of Independent Random Variables ⓘ

Harald Cramér → notableWork → Limit Laws for Sums of Independent Random Variables ⓘ

this entity surface form: Random Variables and Probability Distributions

Paul Lévy → notableWork → Limit Laws for Sums of Independent Random Variables ⓘ

this entity surface form: Théorie de l’addition des variables aléatoires

Soviet school of probability theory → notableWork → Limit Laws for Sums of Independent Random Variables ⓘ

this entity surface form: limit theorems in probability