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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 90–109 (Mi tvp2999)  

This article is cited in 17 scientific papers (total in 17 papers)

Merging to semistable laws

S. Csörgöa, Z. Megyesiab

a University of Szeged
b University of Michigan

Abstract: We show that, despite the lack of asymptotic distributions in the usual sense, the distribution functions of suitably centered and normalized partial sums of independent and identically distributed random variables from the domain of geometric partial attraction of a semistable law merge together uniformly with a family of semistable distribution functions. More generally, even the corresponding, possibly lightly trimmed sums merge. Analogous merge results hold also for sample extremes. The main result is illustrated on generalized St. Petersburg games.

Keywords: semistable laws, domains of geometric partial attraction, merge, lightly trimmed sums, sample extremes, generalized St. Petersburg games.


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English version:
Theory of Probability and its Applications, 2003, 47:1, 17–33

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Received: 16.08.1999

Citation: S. Csörgö, Z. Megyesi, “Merging to semistable laws”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 90–109; Theory Probab. Appl., 47:1 (2003), 17–33

Citation in format AMSBIB
\by S.~Cs\"org\"o, Z.~Megyesi
\paper Merging to semistable laws
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 1
\pages 90--109
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 17--33

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    This publication is cited in the following articles:
    1. Megyesi Z., “Domains of geometric partial attraction of max-semistable laws: Structure, merge and almost sure limit theorems”, J. Theoret. Probab., 15:4 (2002), 973–1005  crossref  mathscinet  zmath  isi  scopus
    2. Berkes I., Csaki E., Csorgo S., Megyesi Z., “Almost sure limit theorems for sums and maxima from the domain of geometric partial attraction of semistable laws”, Limit Theorems in Probability and Statistics, I (2002), 133–157  mathscinet  zmath  isi
    3. Scheffler H.-P., “Precise asymptotics in Spitzer and Baum–Katz's law of large numbers: the semistable case”, J. Math. Anal. Appl., 288:1 (2003), 285–298  crossref  mathscinet  zmath  isi  scopus
    4. Fazekas I., Chuprunov A., “An almost sure functional limit theorem for the domain of geometric partial attraction of semistable laws”, J. Theoret. Probab., 20:2 (2007), 339–353  crossref  mathscinet  zmath  isi  elib  scopus
    5. Csörgő S., “Fourier analysis of semistable distributions”, Acta Appl. Math., 96:1-3 (2007), 159–174  crossref  mathscinet  zmath  isi  scopus
    6. Becker-Kern P., “Almost sure limit theorems of mantissa type for semistable domains of attraction”, Acta Math. Hungar., 114:4 (2007), 301–336  crossref  mathscinet  zmath  isi  scopus
    7. Csörgő S., Kevei P., “Merging asymptotic expansions for cooperative gamblers in generalized St. Petersburg games”, Acta Math. Hungar., 121:1-2 (2008), 119–156  crossref  mathscinet  zmath  isi  scopus
    8. A. N. Chuprunov, L. P. Terekhova, “An almost sure limit theorem for random sums of independent random variables in the domain of attraction of a semistable law”, Russian Math. (Iz. VUZ), 53:11 (2009), 74–76  mathnet  crossref  mathscinet  zmath
    9. Kevei P., Csörgő S., “Merging of linear combinations to semistable laws”, J. Theoret. Probab., 22:3 (2009), 772–790  crossref  mathscinet  zmath  isi  scopus
    10. Kevei P., “Merging asymptotic expansions for semistable random variables”, Lith. Math. J., 49:1 (2009), 40–54  crossref  mathscinet  zmath  isi  scopus
    11. Gyoerfi L., Kevei P., “On the Rate of Convergence of the St. Petersburg Game”, Period Math Hungar, 62:1 (2011), 13–37  crossref  mathscinet  zmath  isi  scopus
    12. Theory Probab. Appl., 56:4 (2011), 621–633  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    13. Ho Dang Phuc, “Domains of Operator Semi-Attraction of Probability Measures on Banach Spaces”, Braz. J. Probab. Stat., 28:4 (2014), 587–611  crossref  mathscinet  zmath  isi  scopus
    14. Theory Probab. Appl., 60:1 (2016), 134–142  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Fukker G., Gyoerfi L., Kevei P., “Asymptotic Behavior of the Generalized St. Petersburg Sum Conditioned on Its Maximum”, Bernoulli, 22:2 (2016), 1026–1054  crossref  mathscinet  zmath  isi  scopus
    16. Chaudhuri R., Pipiras V., “Non-Gaussian Semi-Stable Laws Arising in Sampling of Finite Point Processes”, Bernoulli, 22:2 (2016), 1055–1092  crossref  mathscinet  zmath  isi  scopus
    17. Berkes I., “Strong approximation of the St.?Petersburg game”, Statistics, 51:1 (2017), 3–10  crossref  mathscinet  zmath  isi  scopus
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