Strong approximation of the St. Petersburg game

DOI10.1080/02331888.2016.1269476zbMath1366.60067OpenAlexW2565890248MaRDI QIDQ5276164

István Berkes

Publication date: 14 July 2017

Published in: Statistics (Search for Journal in Brave)

Full work available at URL: http://openlib.tugraz.at/592fe1d74c197

zbMATH Keywords

St. Petersburg gamesemistable lawsa.s. invariance principle

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (1)

Strong approximation and a central limit theorem for St. Petersburg sums

Cites Work

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• The \(m(n)\) out of \(k(n)\) bootstrap for partial sums of St. Petersburg type games
• Non-central limit theorems for random selections
• Fourier analysis of semistable distributions
• Almost sure and weak invariance principles for random variables attracted by a stable law
• Approximation theorems for independent and weakly dependent random vectors
• Almost sure limit theorems for the St. Petersburg game
• A strong approximation theorem for sums of random vectors in the domain of attraction to a stable law
• Tail probabilities of St. Petersburg sums, trimmed sums, and their limit
• Almost sure invariance principles when EX 1 2 =?

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