Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 1, pp. 380 - 395

Let {Xn,n∈Nd} be a random field i.e. a family of random variables indexed by Nd, d≥2. Complete convergence, convergence rates for non-identically distributed,...

Baum–Katz type theorems | Negatively dependent random fields | Fuk–Nagaev inequality | Martingale random fields | Complete convergence | Baum-Katz type theorems | Fuk-Nagaev inequality | MATHEMATICS | MATHEMATICS, APPLIED | RANDOM-VARIABLES | Equality

Baum–Katz type theorems | Negatively dependent random fields | Fuk–Nagaev inequality | Martingale random fields | Complete convergence | Baum-Katz type theorems | Fuk-Nagaev inequality | MATHEMATICS | MATHEMATICS, APPLIED | RANDOM-VARIABLES | Equality

Journal Article

Acta mathematica Hungarica, ISSN 1588-2632, 2016, Volume 151, Issue 1, pp. 162 - 172

We propose an approach to the Baum–Katz theorem for dependent random sequences. Using this result, we obtain the rate of convergence in the strong law of large...

60B12 | Mathematics, general | Mathematics | negatively associated random variable | Rademacher type p Banach space | Baum–Katz theorem | 60F15 | MATHEMATICS | MOMENT INEQUALITIES | Baum-Katz theorem | RANDOM-VARIABLES

60B12 | Mathematics, general | Mathematics | negatively associated random variable | Rademacher type p Banach space | Baum–Katz theorem | 60F15 | MATHEMATICS | MOMENT INEQUALITIES | Baum-Katz theorem | RANDOM-VARIABLES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2020, Volume 484, Issue 1, p. 123662

In this work there is considered complete convergence for widely acceptable random variables under the sub-linear expectations. The presented results are...

Regularly varying function | Complete convergence | Baum-Katz theorem | Sub-linear expectations | Widely acceptable random variables | MATHEMATICS | MATHEMATICS, APPLIED | LAWS | ROSENTHALS INEQUALITIES

Regularly varying function | Complete convergence | Baum-Katz theorem | Sub-linear expectations | Widely acceptable random variables | MATHEMATICS | MATHEMATICS, APPLIED | LAWS | ROSENTHALS INEQUALITIES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2012, Volume 390, Issue 1, pp. 1 - 14

Let X1,X2,… be i.i.d. random variables with partial sums Sn, n⩾1. The now classical Baum–Katz theorem provides necessary and sufficient moment conditions for...

Precise asymptotics | Convergence rates | Law of large numbers | Baum–Katz | Baum-Katz | MATHEMATICS | MATHEMATICS, APPLIED | LAW

Precise asymptotics | Convergence rates | Law of large numbers | Baum–Katz | Baum-Katz | MATHEMATICS | MATHEMATICS, APPLIED | LAW

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2007, Volume 336, Issue 2, pp. 1489 - 1492

We obtain a Baum–Katz–Nagaev type theorem for bounded martingale difference sequences that have more than a second moment, and prove that the celebrated...

Baum–Katz–Nagaev theorem | Martingale difference | Baum-Katz-Nagaev theorem | martingale difference | MATHEMATICS | MATHEMATICS, APPLIED | LARGE DEVIATIONS

Baum–Katz–Nagaev theorem | Martingale difference | Baum-Katz-Nagaev theorem | martingale difference | MATHEMATICS | MATHEMATICS, APPLIED | LARGE DEVIATIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 380, Issue 2, pp. 571 - 584

Let { X n , n ∈ N r } be a random field i.e. a family of random variables indexed by N r , r ⩾ 2 . We discuss complete convergence and convergence rates under...

[formula omitted]-mixing random fields | Negatively associated random fields | Martingale random fields | Complete convergence | Baum–Katz theorem | mixing random fields | Baum-Katz theorem | MARTINGALES | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | rho-mixing random fields | MAXIMUM | ITERATED LOGARITHM | MATHEMATICS | MOMENT INEQUALITIES | PARTIAL-SUMS | SURE CONVERGENCE | INDEPENDENT RANDOM-VARIABLES | INVARIANCE-PRINCIPLE

[formula omitted]-mixing random fields | Negatively associated random fields | Martingale random fields | Complete convergence | Baum–Katz theorem | mixing random fields | Baum-Katz theorem | MARTINGALES | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | rho-mixing random fields | MAXIMUM | ITERATED LOGARITHM | MATHEMATICS | MOMENT INEQUALITIES | PARTIAL-SUMS | SURE CONVERGENCE | INDEPENDENT RANDOM-VARIABLES | INVARIANCE-PRINCIPLE

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 3/2013, Volume 138, Issue 4, pp. 365 - 385

The legendary 1947-paper by Hsu and Robbins, in which the authors introduced the concept of “complete convergence”, generated a series of papers culminating in...

law of large numbers | Baum–Katz | 60G50 | Mathematics, general | 60K05 | 62G20 | Mathematics | 62G10 | convergence rate | Hsu–Robbins | 60F05 | 60F15 | Hsu-Robbins | Baum-Katz | LARGE NUMBERS | INEQUALITIES | MIXING SEQUENCES | THEOREM | SUMS | MATHEMATICS | PROBABILITY | DAVIS LAWS | CONVERGENCE | INDEPENDENT RANDOM-VARIABLES

law of large numbers | Baum–Katz | 60G50 | Mathematics, general | 60K05 | 62G20 | Mathematics | 62G10 | convergence rate | Hsu–Robbins | 60F05 | 60F15 | Hsu-Robbins | Baum-Katz | LARGE NUMBERS | INEQUALITIES | MIXING SEQUENCES | THEOREM | SUMS | MATHEMATICS | PROBABILITY | DAVIS LAWS | CONVERGENCE | INDEPENDENT RANDOM-VARIABLES

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 1/2017, Volume 30, Issue 1, pp. 185 - 216

The present paper is devoted to the study of the hybrids of k-spacing empirical and partial sum processes. In the first part, we present the gaussian...

Precise asymptotics | Complete moment convergence | Spacing empirical process | Convergence rates | Invariance principles | Mathematics | Topology | Order statistics | Geometry | Algebra | Gaussian process | Analysis | Baum–Katz | Primary 62G30 | Mathematics, general | Applications of Mathematics | 60F17 | Hybrid process | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | OF-FIT TESTS | ITERATED LOGARITHM | U-STATISTICS | MOMENT CONVERGENCE | RANDOM-VARIABLES | MATHEMATICS | WEIGHTED BOOTSTRAP | Baum-Katz | Probability | Functional Analysis | Statistics | Statistics Theory

Precise asymptotics | Complete moment convergence | Spacing empirical process | Convergence rates | Invariance principles | Mathematics | Topology | Order statistics | Geometry | Algebra | Gaussian process | Analysis | Baum–Katz | Primary 62G30 | Mathematics, general | Applications of Mathematics | 60F17 | Hybrid process | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | OF-FIT TESTS | ITERATED LOGARITHM | U-STATISTICS | MOMENT CONVERGENCE | RANDOM-VARIABLES | MATHEMATICS | WEIGHTED BOOTSTRAP | Baum-Katz | Probability | Functional Analysis | Statistics | Statistics Theory

Journal Article

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, ISSN 1578-7303, 9/2012, Volume 106, Issue 2, pp. 321 - 331

In the paper, we present some Baum–Katz type results for $${\varphi}$$ -mixing random variables with different distributions. Partial results generalize the...

{\varphi}$$ -Mixing random variables | Complete convergence | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | Baum–Katz theorem | 60F15 | MATHEMATICS | Baum-Katz theorem | SEQUENCES | phi-Mixing random variables | STRONG LAW | CONVERGENCE-RATES | Law

{\varphi}$$ -Mixing random variables | Complete convergence | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | Baum–Katz theorem | 60F15 | MATHEMATICS | Baum-Katz theorem | SEQUENCES | phi-Mixing random variables | STRONG LAW | CONVERGENCE-RATES | Law

Journal Article

ScienceAsia, ISSN 1513-1874, 02/2016, Volume 42, Issue 1, pp. 66 - 74

In this paper, the complete convergence and the complete moment convergence of weighted sums for an array of negatively superadditive dependent random...

Marcinkiewicz-Zygmund type strong law of large numbers | Baum-Katz type theorem | LARGE NUMBERS | ASSOCIATION | MULTIDISCIPLINARY SCIENCES

Marcinkiewicz-Zygmund type strong law of large numbers | Baum-Katz type theorem | LARGE NUMBERS | ASSOCIATION | MULTIDISCIPLINARY SCIENCES

Journal Article

Statistical Papers, ISSN 0932-5026, 11/2014, Volume 55, Issue 4, pp. 1121 - 1143

The present paper is devoted to the study of the hybrids of empirical and partial sums processes. In the first part, we present a synthesis of results related...

Precise asymptotics | Complete moment convergence | Convergence rates | Probability Theory and Stochastic Processes | Empirical processes | Statistics | Gaussian process | Statistics for Business/Economics/Mathematical Finance/Insurance | Primary: 62G30 | Operations Research/Decision Theory | Baum–Katz | Strong approximations | Economic Theory | Partial sums | Weighted bootstrap processes | 60F17 | COMPLETE CONVERGENCE | LARGE NUMBERS | LAW | APPROXIMATIONS | STATISTICS & PROBABILITY | ITERATED LOGARITHM | RANDOM-VARIABLES | MOMENT CONVERGENCE | Baum-Katz | BOOTSTRAP METHODS | Analysis | Convergence (Social sciences) | Gaussian processes | Studies | Theorems | Bootstrap method | Mathematical models | Mathematics | Law | Synthesis | Asymptotic properties | Logarithms | Empirical analysis | Joints | Convergence | Sums | Probability | Functional Analysis | Statistics Theory

Precise asymptotics | Complete moment convergence | Convergence rates | Probability Theory and Stochastic Processes | Empirical processes | Statistics | Gaussian process | Statistics for Business/Economics/Mathematical Finance/Insurance | Primary: 62G30 | Operations Research/Decision Theory | Baum–Katz | Strong approximations | Economic Theory | Partial sums | Weighted bootstrap processes | 60F17 | COMPLETE CONVERGENCE | LARGE NUMBERS | LAW | APPROXIMATIONS | STATISTICS & PROBABILITY | ITERATED LOGARITHM | RANDOM-VARIABLES | MOMENT CONVERGENCE | Baum-Katz | BOOTSTRAP METHODS | Analysis | Convergence (Social sciences) | Gaussian processes | Studies | Theorems | Bootstrap method | Mathematical models | Mathematics | Law | Synthesis | Asymptotic properties | Logarithms | Empirical analysis | Joints | Convergence | Sums | Probability | Functional Analysis | Statistics Theory

Journal Article

Stochastics and Dynamics, ISSN 0219-4937, 04/2017, Volume 17, Issue 2

Liu and Lin (Statist. Probab. Lett. 2006) introduced a kind of complete moment convergence which includes complete convergence as a special case. In this...

precise asymptotics | Convergence rate | complete moment convergence | MARTINGALES | MULTIDIMENSIONAL INDEXES | LARGE NUMBERS | SERIES | STATISTICS & PROBABILITY | ITERATED LOGARITHM | RANDOM-VARIABLES | BAUM-KATZ | STRONG LAW | PROBABILITIES

precise asymptotics | Convergence rate | complete moment convergence | MARTINGALES | MULTIDIMENSIONAL INDEXES | LARGE NUMBERS | SERIES | STATISTICS & PROBABILITY | ITERATED LOGARITHM | RANDOM-VARIABLES | BAUM-KATZ | STRONG LAW | PROBABILITIES

Journal Article

Advances in applied probability, ISSN 0001-8678, 07/2016, Volume 48, Issue A, pp. 181 - 201

Starting with independent, identically distributed random variables X 1,X 2... and their partial sums (S n ), together with a nondecreasing sequence (b(n)), we...

large deviations | EXCESS | LARGE NUMBERS | LAW | INEQUALITIES | Fuk-Nagaev inequality | STATISTICS & PROBABILITY | RATES | moments | complete convergence | SAMPLE-SUMS | Baum-Katz theorem | THEOREMS | counting variables | BOUNDARY CROSSINGS | INDEPENDENT RANDOM-VARIABLES | Independent variables | Random variables | Convergence

large deviations | EXCESS | LARGE NUMBERS | LAW | INEQUALITIES | Fuk-Nagaev inequality | STATISTICS & PROBABILITY | RATES | moments | complete convergence | SAMPLE-SUMS | Baum-Katz theorem | THEOREMS | counting variables | BOUNDARY CROSSINGS | INDEPENDENT RANDOM-VARIABLES | Independent variables | Random variables | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2000, Volume 248, Issue 1, pp. 233 - 246

Let X,X1,X2,… be a sequence of i.i.d. random variables such that EX=0, let Z be a random variable possessing a stable distribution G with exponent α, 1<α≤2,...

stable distributions | Fuk–Nagaev type inequality | Marcinkiewicz–Zygmund law | Davis law | Baum–Katz law | tail probabilities of sums of i.i.d. random variables | Katz law | Nagaev type inequality | Baum | Zygmund law | Fuk | Marcinkiewicz | Tail probabilities of sums of i.i.d. random variables | Baum-Katz law | Stable distributions | Fuk-Nagaev type inequality | Marcinkiewicz-Zygmund law | MATHEMATICS | MATHEMATICS, APPLIED

stable distributions | Fuk–Nagaev type inequality | Marcinkiewicz–Zygmund law | Davis law | Baum–Katz law | tail probabilities of sums of i.i.d. random variables | Katz law | Nagaev type inequality | Baum | Zygmund law | Fuk | Marcinkiewicz | Tail probabilities of sums of i.i.d. random variables | Baum-Katz law | Stable distributions | Fuk-Nagaev type inequality | Marcinkiewicz-Zygmund law | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 02/2017, Volume 46, Issue 4, pp. 1731 - 1743

In this paper, we study the Toeplitz lemma, the Cesàro mean convergence theorem, and the Kronecker lemma. At first, we study "complete convergence" versions of...

Cesàro mean convergence theorem | Kronecker lemma | complete convergence | Toeplitz lemma | complete moment convergence | 60F25 | LAW | SEQUENCES | STATISTICS & PROBABILITY | INDEPENDENT RANDOM ELEMENTS | RANDOM-VARIABLES | WEIGHTED SUMS | RATES | MOVING-AVERAGE PROCESSES | Cesaro mean convergence theorem | 40A05 | PRECISE ASYMPTOTICS | 60F05 | 60F15 | BAUM-KATZ THEOREM | Theorems | Statistical methods | Statistics | Convergence

Cesàro mean convergence theorem | Kronecker lemma | complete convergence | Toeplitz lemma | complete moment convergence | 60F25 | LAW | SEQUENCES | STATISTICS & PROBABILITY | INDEPENDENT RANDOM ELEMENTS | RANDOM-VARIABLES | WEIGHTED SUMS | RATES | MOVING-AVERAGE PROCESSES | Cesaro mean convergence theorem | 40A05 | PRECISE ASYMPTOTICS | 60F05 | 60F15 | BAUM-KATZ THEOREM | Theorems | Statistical methods | Statistics | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 9

For a sequence of i.i.d. random variables { X , X n , n ≥ 1 } $\{X, X_{n}, n\ge1\}$ and a sequence of positive real numbers { a n , n ≥ 1 } $\{a_{n}, n\ge1\}$...

complete convergence | Baum-Katz theorem | Analysis | general moment condition | Mathematics, general | Mathematics | Applications of Mathematics | strong law of large numbers | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | Texts | Theorems | Random variables | Real numbers | Inequalities | Convergence

complete convergence | Baum-Katz theorem | Analysis | general moment condition | Mathematics, general | Mathematics | Applications of Mathematics | strong law of large numbers | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | Texts | Theorems | Random variables | Real numbers | Inequalities | Convergence

Journal Article

17.
Full Text
A note on complete convergence of weighted sums for array of rowwise AANA random variables

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 13

In this paper, we consider complete convergence and complete moment convergence of weighted sums for an array of rowwise AANA random variables. The main result...

complete convergence | Baum-Katz theorem | Analysis | AANA random variable | Mathematics, general | Mathematics | Applications of Mathematics | Marcinkiewicz-Zygmund type strong law of large numbers | Complete convergence | MATHEMATICS | RATES | MATHEMATICS, APPLIED | LARGE NUMBERS | STRONG LAW

complete convergence | Baum-Katz theorem | Analysis | AANA random variable | Mathematics, general | Mathematics | Applications of Mathematics | Marcinkiewicz-Zygmund type strong law of large numbers | Complete convergence | MATHEMATICS | RATES | MATHEMATICS, APPLIED | LARGE NUMBERS | STRONG LAW

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2012, Volume 2012, Issue 1, pp. 1 - 8

Let be a sequence of i.i.d. random variables with zero mean, set , , and . In this paper, the authors discuss the rate of approximation of by under suitable...

Analysis | random variable | Mathematics, general | Mathematics | Applications of Mathematics | convergence rate | theorem of Heyde | Convergence rate | Theorem of Heyde | i.i.d. random variable | MATHEMATICS | MATHEMATICS, APPLIED | LAWS | LARGE NUMBERS | BAUM-KATZ | PRECISE ASYMPTOTICS

Analysis | random variable | Mathematics, general | Mathematics | Applications of Mathematics | convergence rate | theorem of Heyde | Convergence rate | Theorem of Heyde | i.i.d. random variable | MATHEMATICS | MATHEMATICS, APPLIED | LAWS | LARGE NUMBERS | BAUM-KATZ | PRECISE ASYMPTOTICS

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 11/2014, Volume 94, pp. 63 - 68

For a sequence of i.i.d. random variables {X,Xn,n≥1} with EX=0 and Eexp{(log|X|)α}<∞ for some α>1, Gut and Stadtmüller (2011) proved a Baum–Katz theorem. In...

Convergence rates | Baum–Katz law | Sums of i.i.d. random variables | Baum-Katz law | STATISTICS & PROBABILITY

Convergence rates | Baum–Katz law | Sums of i.i.d. random variables | Baum-Katz law | STATISTICS & PROBABILITY

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 6, pp. 1803 - 1809

Let { X , X n ; n ≥ 1 } be a sequence of independent and identically distributed (i.i.d.) random variables with X in the domain of attraction of the normal law...

Precise asymptotics | Self-normalized sums | Complete moment convergence | RATES | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | BAUM-KATZ | ITERATED LOGARITHM | RANDOM-VARIABLES | DEVIATIONS | Attraction | Mathematical models | Law | Random variables | Convergence | Sums

Precise asymptotics | Self-normalized sums | Complete moment convergence | RATES | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | BAUM-KATZ | ITERATED LOGARITHM | RANDOM-VARIABLES | DEVIATIONS | Attraction | Mathematical models | Law | Random variables | Convergence | Sums

Journal Article

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