Generalization and Refinement of the Integro-Local Stone Theorem for Sums of Random Vectors

DOI10.1137/S0040585X97T988368zbMath1377.60058OpenAlexW2778013189MaRDI QIDQ4602298

Aleksandr A. Borovkov

Publication date: 9 January 2018

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t988368

zbMATH Keywords

integro-local Stone theoremsums of random vectorstriangular array schemebound for remainder term

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (5)

Edgeworth expansions for independent bounded integer valued random variables ⋮ Integro-Local CLT for Sums of Independent Nonlattice Random Vectors ⋮ A refined version of the integro-local Stone theorem ⋮ On Integro-Local CLT for Sums of Independent Random Vectors ⋮ Integro-Local Limit Theorems for Compound Renewal Processes

Cites Work

• Probability theory. Edited by K. A. Borovkov. Transl. from the Russian by O. Borovkova and P. S. Ruzankin
• On a Local Limit Theorem for Integer Random Vectors
• Integro-Local and Local Theorems on Normal and Large Deviations of the Sums of Nonidentically Distributed Random Variables in the Triangular Array Scheme
• On the Distribution of the First Passage Time of a Random Walk to an Arbitrary Remote Boundary
• A Local Limit Theorem for Nonlattice Multi-Dimensional Distribution Functions
• A Local Limit Theorem
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