Statistical convergence of a sequence of random variables and limit theorems.

DOI10.1007/s10492-013-0021-7zbMath1289.40015OpenAlexW1976082692MaRDI QIDQ375446

Sanjoy Kr. Ghosal

Publication date: 30 October 2013

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10338.dmlcz/143339

zbMATH Keywords

statistical convergenceasymptotic densityrandom variablestatistical convergence in distributionstatistical convergence in mean of order \(r\)

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Limit theorems in probability theory (60F99) Ideal and statistical convergence (40A35)

Related Items (22)

Weighted modulus \(S_\theta\)-convergence of order \(\alpha\) in probability ⋮ Generalized weighted random convergence in probability ⋮ Unnamed Item ⋮ On Δvm(f)–statistical convergence of orderα ⋮ Statistical extension of bounded sequence space ⋮ On the concept of \(B\)-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense ⋮ Characterization of rough weighted statistical limit set ⋮ A notion of $\alpha\beta$-statistical convergence of order $\gamma$ in probability ⋮ On (λ,f)-statistical boundedness of order α ⋮ Rough statistical convergence of a sequence of random variables in probability ⋮ Applications of statistically probability convergence to approximation theorem ⋮ On the concept of \(A\)-statistical uniform integrability and the law of large numbers ⋮ \(\mathcal I\)-statistical convergence of a sequence of random variables in probability ⋮ Unnamed Item ⋮ Weighted statistical convergence of order \(\alpha\) and its applications ⋮ Statistical convergence of order \(\alpha\) in probability ⋮ Unnamed Item ⋮ Different types of quasi-weighted αβ-statistical convergence in probability ⋮ \(S_\lambda\)-convergence of a sequence of random variables ⋮ Some results concerning ideal and classical uniform integrability and mean convergence ⋮ Different behaviors of rough weighted statistical limit set under unbounded moduli ⋮ Effects on rough I-lacunary statistical convergence to induce the weighted sequence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Statistical convergence and ideal convergence for sequences of functions
• Statistical properties of Lorentz gas with periodic configuration of scatterers
• Tauberian theorems via statistical convergence
• Some approximation theorems via statistical convergence.
• Weak laws of large numbers in geometric probability
• On statistical limit points
• Statistical Limit Points
• The Integrability of Certain Functions and Related Summability Methods
• Sur Les Densités de Certaines Suites D'Entiers
• ON STATISTICAL CONVERGENCE
• Statistical convergence in a locally convex space
• Statistical limit superior and limit inferior
• Statistical cluster points and turnpike^*
• A Measure Theoretical Subsequence Characterization of Statistical Convergence
• Sur la convergence statistique
• On statistically convergent sequences of fuzzy numbers

This page was built for publication: Statistical convergence of a sequence of random variables and limit theorems.