One-sided strong laws for increments of sums of i.i.d. random variables

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One-sided strong laws for increments of sums of i.i.d. random variables. / Frolov, A. N.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 39, No. 3-4, 2002, p. 333-359.

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Frolov, A. N. / One-sided strong laws for increments of sums of i.i.d. random variables. In: Studia Scientiarum Mathematicarum Hungarica. 2002 ; Vol. 39, No. 3-4. pp. 333-359.

BibTeX

@article{bf2804873ddd48c4804a6371922e0746,

title = "One-sided strong laws for increments of sums of i.i.d. random variables",

abstract = "We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdos-R{\'e}nyi law of large numbers, the Shepp law, one-sided versions of the Cs{\"o}rgo-R{\'e}v{\'e}sz strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index α ∈ (1,2).",

keywords = "Erd{\"o}s-R{\'e}nyi law, Increments, Law of large numbers, Law of the iterated logarithm, One-sided strong laws, Sums of independent random variables",

author = "Frolov, {A. N.}",

year = "2002",

doi = "10.1556/SScMath.39.2002.3-4.6",

language = "English",

volume = "39",

pages = "333--359",

journal = "Studia Scientiarum Mathematicarum Hungarica",

issn = "0081-6906",

publisher = "Akademiai Kiado",

number = "3-4",

}

RIS

TY - JOUR

T1 - One-sided strong laws for increments of sums of i.i.d. random variables

AU - Frolov, A. N.

PY - 2002

Y1 - 2002

N2 - We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdos-Rényi law of large numbers, the Shepp law, one-sided versions of the Csörgo-Révész strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index α ∈ (1,2).

AB - We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdos-Rényi law of large numbers, the Shepp law, one-sided versions of the Csörgo-Révész strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index α ∈ (1,2).

KW - Erdös-Rényi law

KW - Increments

KW - Law of large numbers

KW - Law of the iterated logarithm

KW - One-sided strong laws

KW - Sums of independent random variables

UR - http://www.scopus.com/inward/record.url?scp=0142233507&partnerID=8YFLogxK

U2 - 10.1556/SScMath.39.2002.3-4.6

DO - 10.1556/SScMath.39.2002.3-4.6

M3 - Article

AN - SCOPUS:0142233507

VL - 39

SP - 333

EP - 359

JO - Studia Scientiarum Mathematicarum Hungarica

JF - Studia Scientiarum Mathematicarum Hungarica

SN - 0081-6906

IS - 3-4

ER -

ID: 75021190