Stochastic Processes and their Applications, ISSN 0304-4149, 05/2017, Volume 127, Issue 5, pp. 1622 - 1636

In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables...

Normal approximation | Wasserstein distance | Malliavin–Stein approach | Rademacher functional | Almost sure central limit theorem | STEINS METHOD | SEQUENCES | Malliavin-Stein approach | STATISTICS & PROBABILITY | Mathematics - Probability

Normal approximation | Wasserstein distance | Malliavin–Stein approach | Rademacher functional | Almost sure central limit theorem | STEINS METHOD | SEQUENCES | Malliavin-Stein approach | STATISTICS & PROBABILITY | Mathematics - Probability

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2015, Volume 2015, Issue 1, pp. 1 - 8

.... In this paper, we are concerned with the almost sure local central limit theorem of parallel to F-n parallel to and sup0(<= t <= 1) F-n...

uniform empirical process | almost sure central limit theorem | almost sure local central limit theorem | DEPENDENT RANDOM-VARIABLES | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL-SUMS | Texts | Theorems | Random variables | Empirical analysis | Inequalities

uniform empirical process | almost sure central limit theorem | almost sure local central limit theorem | DEPENDENT RANDOM-VARIABLES | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL-SUMS | Texts | Theorems | Random variables | Empirical analysis | Inequalities

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1, pp. 1 - 14

..., we get the almost sure central limit theorem for the products of the some partial sums (∏i=1kSk,i(k−1)nμn)μβVk\(({\frac{\prod_{i=1}^{k}S_{k,i}}{(k-1)^{n}\mu ^{n}} )^{\frac{\mu}{\beta V_{k}}} }\), where β>0\(\beta>0...

Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables

Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables

Journal Article

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

The almost sure central limit theorems for the maxima of strongly dependent stationary Gaussian vector sequences are proved under some mild conditions...

Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | strongly dependent stationary Gaussian vector sequences | weight sequence | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | PARTIAL-SUMS | CONVERGENCE | Theorems | Gaussian | Vectors (mathematics) | Mathematical analysis | Maxima | Inequalities

Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | strongly dependent stationary Gaussian vector sequences | weight sequence | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | PARTIAL-SUMS | CONVERGENCE | Theorems | Gaussian | Vectors (mathematics) | Mathematical analysis | Maxima | Inequalities

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 12/2016, Volume 26, Issue 6, pp. 3659 - 3698

.... We prove a functional central limit theorem stating that as n → ∞ the process ${D_n}\left( u \right): = {m^{\frac{1}{2}n}}\left( {{W_\infty }\left( {\frac{u}{{\sqrt n...

Central limit theorem | Mathematical theorems | Analytic functions | Random walk | Conditional convergence | Random variables | Particle intensity | Martingales | Probabilities | Continuous functions | Gaussian analytic function | Random recursive trees | Branching random walk | Functional central limit theorem | Binary search trees | Pólya urns | Stable convergence | Quicksort distribution | Almost sure weak convergence | Galton-Watson processes | Mixing convergence | MARTINGALES | mixing convergence | STATISTICS & PROBABILITY | functional central limit theorem | RANDOM-VARIABLES | almost sure weak convergence | binary search trees | random recursive trees | stable convergence | Polya urns | ZEROS

Central limit theorem | Mathematical theorems | Analytic functions | Random walk | Conditional convergence | Random variables | Particle intensity | Martingales | Probabilities | Continuous functions | Gaussian analytic function | Random recursive trees | Branching random walk | Functional central limit theorem | Binary search trees | Pólya urns | Stable convergence | Quicksort distribution | Almost sure weak convergence | Galton-Watson processes | Mixing convergence | MARTINGALES | mixing convergence | STATISTICS & PROBABILITY | functional central limit theorem | RANDOM-VARIABLES | almost sure weak convergence | binary search trees | random recursive trees | stable convergence | Polya urns | ZEROS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 15

We prove some almost sure central limit theorems for the maxima of strongly dependent nonstationary Gaussian vector sequences under some mild conditions...

strongly dependent nonstationary Gaussian vector sequences | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | weight sequence | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | PARTIAL-SUMS | CONVERGENCE | Theorems | Gaussian | Vectors (mathematics) | Mathematical analysis | Maxima | Inequalities

strongly dependent nonstationary Gaussian vector sequences | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | weight sequence | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | PARTIAL-SUMS | CONVERGENCE | Theorems | Gaussian | Vectors (mathematics) | Mathematical analysis | Maxima | Inequalities

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 15

Let X, X-1, X-2, ... be a standardized Gaussian sequence. The universal results in almost sure central limit theorems for the maxima M-n and partial sums and maxima (S-n/sigma(n), M-n...

standardized Gaussian sequence | partial sums and maxima | almost sure central limit theorem | maxima | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | VERSIONS | MOMENTS | Texts | Theorems | Gaussian | Maxima | Inequalities | Sums

standardized Gaussian sequence | partial sums and maxima | almost sure central limit theorem | maxima | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | VERSIONS | MOMENTS | Texts | Theorems | Gaussian | Maxima | Inequalities | Sums

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 16

.... Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k) 60E15 | Analysis | Products of partial sums | Mathematics, general | Mathematics | Applications of Mathematics | Almost sure global central limit theorem | Negative association | 60F15 | Almost sure local central limit theorem | WEIGHTED SUMS | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | Coefficient of variation | Theorems | Random variables | Research

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 12

Considering a sequence of i.i.d. positive random variables, for products of sums of partial sums we establish an almost sure central limit theorem, which holds...

products of sums of partial sums | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | 60F15 | unbounded measurable functions | MATHEMATICS | MATHEMATICS, APPLIED | Theorems | Random variables | Inequalities | Sums

products of sums of partial sums | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | 60F15 | unbounded measurable functions | MATHEMATICS | MATHEMATICS, APPLIED | Theorems | Random variables | Inequalities | Sums

Journal Article

10.
Full Text
An almost sure central limit theorem of products of partial sums for ρ--mixing sequences

Journal of inequalities and applications, ISSN 1029-242X, 2012, Volume 2012, Issue 1, pp. 1 - 13

< ∞. Denote and the coefficient of variation. Under suitable conditions, by the central limit theorem of weighted sums and the moment inequality we show that where with...

products of partial sums | Analysis | ρ - -mixing | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | Almost sure central limit theorem | mixing | Products of partial sums

products of partial sums | Analysis | ρ - -mixing | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | Almost sure central limit theorem | mixing | Products of partial sums

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 18

In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large...

order statistics | complete convergence | Analysis | 62G30 | Mathematics, general | Mathematics | Applications of Mathematics | large deviation principle | uniform distribution | almost sure central limit theorem | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | LAWS | Theorems | Statistical methods | Statistical analysis | Random variables | Research

order statistics | complete convergence | Analysis | 62G30 | Mathematics, general | Mathematics | Applications of Mathematics | large deviation principle | uniform distribution | almost sure central limit theorem | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | LAWS | Theorems | Statistical methods | Statistical analysis | Random variables | Research

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 376, Issue 1, pp. 29 - 41

... . In this paper we show that the almost sure central limit theorem for self-normalized products of sums holds only under the assumptions that X belongs to the domain...

Domain of attraction of the normal law | Almost sure central limit theorem | Products of sums | Self-normalized | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTICS | ASSOCIATION

Domain of attraction of the normal law | Almost sure central limit theorem | Products of sums | Self-normalized | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTICS | ASSOCIATION

Journal Article

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 5, pp. 1413 - 1422

.... A universal result in almost sure central limit theorem for the self-normalized partial sums 𝑆 /𝑉...

Partial sums | Central limit theorem | Random variables | Self-normalized partial sums | Almost sure central limit theorem | Negatively associated random variables | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-CONVERGENCE

Partial sums | Central limit theorem | Random variables | Self-normalized partial sums | Almost sure central limit theorem | Negatively associated random variables | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-CONVERGENCE

Journal Article

Stochastic processes and their applications, ISSN 0304-4149, 2010, Volume 120, Issue 9, pp. 1607 - 1628

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields...

Hermite power variation | Multiple stochastic integrals | Fractional Brownian motion | Almost sure limit theorem | GAUSSIAN FIELDS | CONVERGENCE | STATISTICS & PROBABILITY | FUNCTIONALS | Almost sure limit theorem Multiple stochastic integrals Fractional Brownian motion Hermite power variation | Probability | Mathematics

Hermite power variation | Multiple stochastic integrals | Fractional Brownian motion | Almost sure limit theorem | GAUSSIAN FIELDS | CONVERGENCE | STATISTICS & PROBABILITY | FUNCTIONALS | Almost sure limit theorem Multiple stochastic integrals Fractional Brownian motion Hermite power variation | Probability | Mathematics

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 9, pp. 2639 - 2644

... . Then an almost sure central limit theorem for self-normalized partial sums S n / V n is studied under a mild condition in this paper.

Central limit theorem | Domain of attraction of the normal law | Almost sure | Self-normalized | DEPENDENT RANDOM-VARIABLES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LARGE DEVIATIONS | Attraction | Theorems | Law | Mathematical models | Random variables | Variance | Sums

Central limit theorem | Domain of attraction of the normal law | Almost sure | Self-normalized | DEPENDENT RANDOM-VARIABLES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LARGE DEVIATIONS | Attraction | Theorems | Law | Mathematical models | Random variables | Variance | Sums

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 9/2016, Volume 110, Issue 2, pp. 699 - 710

.... A universal result in almost sure central limit theorem for the self-normalized partial sums $$S_n/V_n...

Almost sure central limit theorem | Theoretical, Mathematical and Computational Physics | Self-normalized partial sums | Mathematics, general | Mathematics | Applications of Mathematics | Maxima | 60F15 | MATHEMATICS | GAUSSIAN SEQUENCES | PRODUCTS | RANDOM-VARIABLES | Theorems | Mathematical analysis | Texts | Random variables | Formulas (mathematics) | Sums

Almost sure central limit theorem | Theoretical, Mathematical and Computational Physics | Self-normalized partial sums | Mathematics, general | Mathematics | Applications of Mathematics | Maxima | 60F15 | MATHEMATICS | GAUSSIAN SEQUENCES | PRODUCTS | RANDOM-VARIABLES | Theorems | Mathematical analysis | Texts | Random variables | Formulas (mathematics) | Sums

Journal Article

Probability and Mathematical Statistics, ISSN 0208-4147, 2015, Volume 35, Issue 2, pp. 285 - 300

We will investigate an almost sure central limit theorem (ASCLT) for sequences of random variables having the form of a ratio of two terms such that the...

Fractional ornstein–uhlenbeck process | Least squares estimator | Multiple stochastic integrals | Almost sure central limit theorem | multiple stochastic integrals | CONVERGENCE | STATISTICS & PROBABILITY | fractional Ornstein-Uhlenbeck process | least squares estimator

Fractional ornstein–uhlenbeck process | Least squares estimator | Multiple stochastic integrals | Almost sure central limit theorem | multiple stochastic integrals | CONVERGENCE | STATISTICS & PROBABILITY | fractional Ornstein-Uhlenbeck process | least squares estimator

Journal Article

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

.... A universal result in an almost sure limit theorem for the self-normalized products of partial sums is established. MSC: 60F15.

Analysis | self-normalized partial sums | domain of attraction of the normal law | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | MATHEMATICS | MATHEMATICS, APPLIED | I.I.D. RANDOM-VARIABLES | Attraction | Theorems | Law | Random variables | Inequalities | Sums

Analysis | self-normalized partial sums | domain of attraction of the normal law | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | MATHEMATICS | MATHEMATICS, APPLIED | I.I.D. RANDOM-VARIABLES | Attraction | Theorems | Law | Random variables | Inequalities | Sums

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

.... Our goal is to show the unbounded, measurable functions g, which satisfy the almost sure central limit theorem, i.e...

partial sums | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | unbounded measurable functions | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | Theorems | Mathematical analysis | Inequalities | Random variables | Coefficient of variation | Standards | Distribution functions | Sums

partial sums | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | unbounded measurable functions | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | Theorems | Mathematical analysis | Inequalities | Random variables | Coefficient of variation | Standards | Distribution functions | Sums

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 12, pp. 2481 - 2502

.... Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.

60F25 | branching process with immigration | 60F10 | 60J80 | Mathematics | large and moderate deviations | nondegeneration | central limit theorem | random environment | almost sure convergence | Applications of Mathematics | L p convergence and moments | 60F05 | convergence and moments | SUPER-BROWNIAN MOTION | MODERATE | MATHEMATICS, APPLIED | non-degeneration | UPPER LARGE DEVIATIONS | DISTRIBUTIONS | MATHEMATICS | L-p convergence and moments | EXTINCTION | MOMENTS | Probability

60F25 | branching process with immigration | 60F10 | 60J80 | Mathematics | large and moderate deviations | nondegeneration | central limit theorem | random environment | almost sure convergence | Applications of Mathematics | L p convergence and moments | 60F05 | convergence and moments | SUPER-BROWNIAN MOTION | MODERATE | MATHEMATICS, APPLIED | non-degeneration | UPPER LARGE DEVIATIONS | DISTRIBUTIONS | MATHEMATICS | L-p convergence and moments | EXTINCTION | MOMENTS | Probability

Journal Article

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