Limit behaviors for a β -mixing sequence in the St. Petersburg game

• Yu Miao ^[1] ; Qing Yin ^[1] ; Zhen Wang ^[1]
  1. [1] Henan Normal University

     Henan Normal University

     China

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 1, 2024, págs. 161-171
• Idioma: inglés
• DOI: 10.33044/revuma.3364
• Enlaces
  • Texto completo
• Resumen

  • We consider a sequence of non-negative β-mixing random variables {X,Xn:n≥1} from the classical St. Petersburg game. The accumulated gains Sn=X1+X2+⋯+Xn in the St. Petersburg game are studied, and the large deviations and the weak law of large numbers of Sn are obtained.

• Referencias bibliográficas
  • H. Berbee, Convergence rates in the strong law for bounded mixing sequences, Probab. Theory Related Fields 74 no. 2 (1987), 255–270. DOI MR...
  • R. C. Bradley, Basic properties of strong mixing conditions, in Dependence in probability and statistics (Oberwolfach, 1985), Progr. Probab....
  • Y. S. Chow and H. Robbins, On sums of independent random variables with infinite moments and “fair” games, Proc. Nat. Acad. Sci. U.S.A. 47...
  • S. Csörgő and G. Simons, A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games, Statist. Probab....
  • W. Feller, Note on the law of large numbers and “fair” games, Ann. Math. Statistics 16 (1945), 301–304. DOI MR Zbl
  • Y. Hu and H. Nyrhinen, Large deviations view points for heavy-tailed random walks, J. Theoret. Probab. 17 no. 3 (2004), 761–768. DOI MR Zbl
  • D. Li and Y. Miao, A supplement to the laws of large numbers and the large deviations, Stochastics 93 no. 8 (2021), 1261–1280. DOI MR Zbl
  • Y. Miao, T. Xue, K. Wang, and F. Zhao, Large deviations for dependent heavy tailed random variables, J. Korean Statist. Soc. 41 no. 2 (2012),...
  • G. Schwarz, Finitely determined processes—an indiscrete approach, J. Math. Anal. Appl. 76 no. 1 (1980), 146–158. DOI MR Zbl
  • G. Stoica, Large gains in the St. Petersburg game, C. R. Math. Acad. Sci. Paris 346 no. 9-10 (2008), 563–566. DOI MR Zbl
  • I. Vardi, The St. Petersburg game and continued fractions, C. R. Acad. Sci. Paris Sér. I Math. 324 no. 8 (1997), 913–918. DOI MR Zbl