Limit behaviors for a $\beta$-mixing sequence in the St. Petersburg game

Authors

  • Yu Miao College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China; Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Henan Province, 453007, China
  • Qing Yin College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China
  • Zhen Wang College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China

DOI:

https://doi.org/10.33044/revuma.3364

Abstract

We consider a sequence of non-negative $\beta$-mixing random variables $\{X,X_n : n\geq1\}$ from the classical St. Petersburg game. The accumulated gains $S_n=X_1+X_2+\cdots+X_n$ in the St. Petersburg game are studied, and the large deviations and the weak law of large numbers of $S_n$ are obtained.

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Published

2024-04-24

Issue

Vol. 67 No. 1 (2024)

Section

Article

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Copyright (c) 2024 Yu Miao, Qing Yin, Zhen Wang

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