Almost sure limit theorems for the St. Petersburg game

DOI10.1016/S0167-7152(99)00037-1zbMath0943.60026OpenAlexW2041148266MaRDI QIDQ1805955

István Berkes, Endre Csáki, Sándor Csörgö

Publication date: 4 September 2000

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(99)00037-1

zbMATH Keywords

asymptotic distributionsalmost sure limit theoremsSt. Petersburg game

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Probabilistic games; gambling (91A60)

Related Items

Strong approximation of the St. Petersburg game ⋮ Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum ⋮ A maxtrimmed St. Petersburg game ⋮ A universal result in almost sure central limit theory. ⋮ An almost sure functional limit theorem for the domain of geometric partial attraction of semistable laws ⋮ Tail probabilities of St. Petersburg sums, trimmed sums, and their limit ⋮ A note on the asymptotics of the maxima for the St. Petersburg game ⋮ On the random functional central limit theorems with almost sure convergence for subsequences ⋮ Almost sure limit theorems of mantissa type for semistable domains of attraction ⋮ Exact laws of large numbers for independent Pareto random variables ⋮ An asymmetric St. Petersburg game with trimming

Cites Work

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• On almost sure max-limit theorems
• A note on the almost sure central limit theorem
• Some limit theorems in log density
• A limit theorem which clarifies the ‘Petersburg Paradox'
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
• Almost Sure Convergence in Extreme Value Theory
• The so-called Petersburg paradox
• Note on the Law of Large Numbers and "Fair" Games