Stochastic Processes and their Applications, ISSN 0304-4149, 11/2013, Volume 123, Issue 11, pp. 3919 - 3942

An expansion of large deviation probabilities for martingales is given, which extends the classical result due...

Bernstein’s condition | Central limit theorem | Exponential inequality | Expansions of large deviations | Moderate deviations | Cramér type large deviations | Large deviations | Bernstein's condition | RATES | Cramer type large deviations | CONVERGENCE | STATISTICS & PROBABILITY | PROBABILITIES | Probability | Mathematics

Bernstein’s condition | Central limit theorem | Exponential inequality | Expansions of large deviations | Moderate deviations | Cramér type large deviations | Large deviations | Bernstein's condition | RATES | Cramer type large deviations | CONVERGENCE | STATISTICS & PROBABILITY | PROBABILITIES | Probability | Mathematics

Journal Article

1990, Wiley series in probability and mathematical statistics., ISBN 9780471618560, xiv, 270

Book

Electronic journal of probability, ISSN 1083-6489, 2019, Volume 24

...). We show how to exploit the vector space structure of the tangent spaces to study large deviation properties of geodesic random walks in M...

Large deviations | Riemannian exponential map | Spreading of geodesics | Cramér’s theorem | Geodesic random walks | Jacobi fields | large deviations | spreading of geodesics | Cramer's theorem | STATISTICS & PROBABILITY | geodesic random walks

Large deviations | Riemannian exponential map | Spreading of geodesics | Cramér’s theorem | Geodesic random walks | Jacobi fields | large deviations | spreading of geodesics | Cramer's theorem | STATISTICS & PROBABILITY | geodesic random walks

Journal Article

ADVANCES IN APPLIED PROBABILITY, ISSN 0001-8678, 09/2019, Volume 51, Issue 3, pp. 835 - 864

.... Our approach combines the large deviation techniques from a series of papers by Borovkov and Mogulskii from around 2000 with new auxiliary constructions, enabling us to extend their results...

multivariate ruin problem | RANDOM VECTORS | exact asymptotics | multivariate random walk | LIMIT-THEOREMS | second rate function | INCLUDING LARGE DEVIATIONS | STATISTICS & PROBABILITY | boundary crossing | Cramer moment condition | Large deviation | SUMS | Confidence intervals | Theorems | Theory | Asymptotic properties | Random walk | Smooth boundaries | Probability | Deviation | Multivariate analysis

multivariate ruin problem | RANDOM VECTORS | exact asymptotics | multivariate random walk | LIMIT-THEOREMS | second rate function | INCLUDING LARGE DEVIATIONS | STATISTICS & PROBABILITY | boundary crossing | Cramer moment condition | Large deviation | SUMS | Confidence intervals | Theorems | Theory | Asymptotic properties | Random walk | Smooth boundaries | Probability | Deviation | Multivariate analysis

Journal Article

Journal of applied probability, ISSN 0021-9002, 06/2018, Volume 55, Issue 2, pp. 431 - 449

By extending the methods of Peligrad et al. (2014), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations...

Research Papers | moderate deviation | linear random field | nonparametric regression | Davis-Gut law of the iterated logarithm | Large deviation | REGRESSION | CRAMERS CONDITION | LAW | MOVING AVERAGE PROCESSES | STATISTICS & PROBABILITY | ITERATED LOGARITHM | KERNEL DENSITY-ESTIMATION | RANDOM-VARIABLES | INTEGRAL LIMIT-THEOREMS | ASYMPTOTIC NORMALITY | CONVERGENCE-RATES | Probability | Asymptotic methods | Fields (mathematics)

Research Papers | moderate deviation | linear random field | nonparametric regression | Davis-Gut law of the iterated logarithm | Large deviation | REGRESSION | CRAMERS CONDITION | LAW | MOVING AVERAGE PROCESSES | STATISTICS & PROBABILITY | ITERATED LOGARITHM | KERNEL DENSITY-ESTIMATION | RANDOM-VARIABLES | INTEGRAL LIMIT-THEOREMS | ASYMPTOTIC NORMALITY | CONVERGENCE-RATES | Probability | Asymptotic methods | Fields (mathematics)

Journal Article

1984, CNMS-NSF Regional conference series in applied mathematics, ISBN 9780898711899, Volume 46, v, 75

Book

Stochastic Processes and their Applications, ISSN 0304-4149, 03/2016, Volume 126, Issue 3, pp. 832 - 856

We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric α-stable (0<α<2...

Nonsingular group actions | Point processes | Stable processes | Random fields | Extreme value theory | Large deviations | CRAMERS CONDITION | STATISTICS & PROBABILITY | RANDOM-VARIABLES | SUMS | REGULAR VARIATION | ACCOUNT | INTEGRAL LIMIT-THEOREMS | ERGODIC-THEORY

Nonsingular group actions | Point processes | Stable processes | Random fields | Extreme value theory | Large deviations | CRAMERS CONDITION | STATISTICS & PROBABILITY | RANDOM-VARIABLES | SUMS | REGULAR VARIATION | ACCOUNT | INTEGRAL LIMIT-THEOREMS | ERGODIC-THEORY

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 9, pp. 1939 - 1958

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein’s condition...

伯恩斯坦 | 不等式 | 独立随机变量和 | 概率 | 高斯法 | 大偏差 | 类似 | 60E15 | Hoeffding’s inequality | sharp large deviations | 60F10 | Bennett’s inequality | 60G50 | Mathematics | Cramér large deviations | sums of independent random variables | Bernstein’s inequality | expansion of Bahadur-Rao | Applications of Mathematics | 60F05 | MARTINGALES | MATHEMATICS | Hoeffding's inequality | MATHEMATICS, APPLIED | Bernstein's inequality | Cramer large deviations | PROBABILITY-INEQUALITIES | Bennett's inequality | EXPONENTIAL INEQUALITIES | Resveratrol | Mathematical analysis | China | Inequalities | Gaussian | Random variables | Deviation | Standards | Sums | Probability

伯恩斯坦 | 不等式 | 独立随机变量和 | 概率 | 高斯法 | 大偏差 | 类似 | 60E15 | Hoeffding’s inequality | sharp large deviations | 60F10 | Bennett’s inequality | 60G50 | Mathematics | Cramér large deviations | sums of independent random variables | Bernstein’s inequality | expansion of Bahadur-Rao | Applications of Mathematics | 60F05 | MARTINGALES | MATHEMATICS | Hoeffding's inequality | MATHEMATICS, APPLIED | Bernstein's inequality | Cramer large deviations | PROBABILITY-INEQUALITIES | Bennett's inequality | EXPONENTIAL INEQUALITIES | Resveratrol | Mathematical analysis | China | Inequalities | Gaussian | Random variables | Deviation | Standards | Sums | Probability

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 11/2013, Volume 351, Issue 21-22, pp. 845 - 848

We improve Bernsteinʼs inequality for sums of non-bounded random variables. In particular, we establish a sharp large deviation expansion similar to that of Cramér and Bahadur–Rao. Nous améliorons lʼinégalité...

MATHEMATICS

MATHEMATICS

Journal Article

Abstract and applied analysis, ISSN 1085-3375, 4/2014, Volume 2014, pp. 1 - 9

...) random array, and then upper and lower bounds for precise large deviations of nonrandom and random sums of random variables with dominated variation are investigated...

MATHEMATICS | CRAMERS CONDITION | ACCOUNT | CONSISTENTLY VARYING TAILS | LOWER BOUNDS | INSURANCE | RANDOM SUMS | RENEWAL RISK MODEL | INTEGRAL LIMIT THEOREMS | HOLD | RANDOM-VARIABLES | Usage | Models | Mathematical models | Insurance | Risk assessment | Studies | Science | Random variables | Research | Risk management | Arrays

MATHEMATICS | CRAMERS CONDITION | ACCOUNT | CONSISTENTLY VARYING TAILS | LOWER BOUNDS | INSURANCE | RANDOM SUMS | RENEWAL RISK MODEL | INTEGRAL LIMIT THEOREMS | HOLD | RANDOM-VARIABLES | Usage | Models | Mathematical models | Insurance | Risk assessment | Studies | Science | Random variables | Research | Risk management | Arrays

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2015, Volume 28, Issue 4, pp. 1556 - 1570

... uniformly in x ∈[ 0 , o (λ 1 / 6 )) ,a s λ →∞ . Keywords Cramér large deviation · Self-normalized compound Poisson sum · Studentized compound Poisson sum Mathematics...

Cramér large deviation | 62E20 | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Self-normalized compound Poisson sum | Studentized compound Poisson sum | LIMIT-THEOREMS | APPROXIMATIONS | RISK | STATISTICS & PROBABILITY | Cramer large deviation | RANDOM-VARIABLES

Cramér large deviation | 62E20 | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Self-normalized compound Poisson sum | Studentized compound Poisson sum | LIMIT-THEOREMS | APPROXIMATIONS | RISK | STATISTICS & PROBABILITY | Cramer large deviation | RANDOM-VARIABLES

Journal Article

Discrete Mathematics and Applications, ISSN 0924-9265, 12/2017, Volume 27, Issue 6, pp. 361 - 376

.... It is shown that the supplement of immigration to critical or supercritical processes results only in the change of multiplicative constant in the asymptotics of large deviation probabilities ≥ exp...

random walks | Large deviations | random environments | Cramér condition | processes with immigration | branching processes | Cramr condition | Branching processes | Random environments | Random walks | Processes with immigration | Emigration and immigration

random walks | Large deviations | random environments | Cramér condition | processes with immigration | branching processes | Cramr condition | Branching processes | Random environments | Random walks | Processes with immigration | Emigration and immigration

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2012, Volume 25, Issue 4, pp. 913 - 924

In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions...

60F10 | Precise large deviations | Heavy tails | Probability Theory and Stochastic Processes | 60K05 | Mathematics | Random sums | Statistics, general | Long-tailed distribution | 60F05 | CRAMERS CONDITION | ACCOUNT | STATISTICS & PROBABILITY | MODEL | INTEGRAL LIMIT THEOREMS | INDEPENDENT RANDOM-VARIABLES | HOLD

60F10 | Precise large deviations | Heavy tails | Probability Theory and Stochastic Processes | 60K05 | Mathematics | Random sums | Statistics, general | Long-tailed distribution | 60F05 | CRAMERS CONDITION | ACCOUNT | STATISTICS & PROBABILITY | MODEL | INTEGRAL LIMIT THEOREMS | INDEPENDENT RANDOM-VARIABLES | HOLD

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 12, pp. 2465 - 2480

We show large deviation expansions for sums of independent and bounded from above random variables...

60E15 | Cramér large deviations | Hoeffding’s inequality | sums of independent random variables | sharp large deviations | 60F10 | 60G50 | Mathematics | Applications of Mathematics | Talagrand’s inequality | 60F05 | MARTINGALES | MATHEMATICS | Hoeffding's inequality | MATHEMATICS, APPLIED | Talagrand's inequality | Cramer large deviations | HOEFFDINGS INEQUALITIES | PROBABILITY-INEQUALITIES | INDEPENDENT RANDOM-VARIABLES

60E15 | Cramér large deviations | Hoeffding’s inequality | sums of independent random variables | sharp large deviations | 60F10 | 60G50 | Mathematics | Applications of Mathematics | Talagrand’s inequality | 60F05 | MARTINGALES | MATHEMATICS | Hoeffding's inequality | MATHEMATICS, APPLIED | Talagrand's inequality | Cramer large deviations | HOEFFDINGS INEQUALITIES | PROBABILITY-INEQUALITIES | INDEPENDENT RANDOM-VARIABLES

Journal Article

15.
Full Text
Berry-Esseen bounds and Cramér type large deviations for eigenvalues of random matrices

中国科学：数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 9, pp. 1959 - 1980

We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases...

维格纳 | 随机矩阵 | 厄米特矩阵 | 协方差矩阵 | R型 | Berry-Esseen界 | 特征值 | 大偏差 | 15A52 | eigenvalues | random matrices | Berry-Esseen bounds | 60F10 | Mathematics | Applications of Mathematics | Cramér type large deviations | 15A18 | Covariance | Matrices (mathematics) | Mathematical analysis | China | Eigenvalues | Deviation | Matrix methods

维格纳 | 随机矩阵 | 厄米特矩阵 | 协方差矩阵 | R型 | Berry-Esseen界 | 特征值 | 大偏差 | 15A52 | eigenvalues | random matrices | Berry-Esseen bounds | 60F10 | Mathematics | Applications of Mathematics | Cramér type large deviations | 15A18 | Covariance | Matrices (mathematics) | Mathematical analysis | China | Eigenvalues | Deviation | Matrix methods

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 2017, Volume 22

.... To refine these results, Chen, Fang and Shao prove Cramer type moderate deviation theorems for non-critical cases by using Stein method...

Curie-Weiss model | Cramér type moderate deviation | Cramer type moderate deviation | STEINS METHOD | TESTS | STATISTICS & PROBABILITY | RANDOM-VARIABLES | Probability | Mathematical Physics | Mathematics

Curie-Weiss model | Cramér type moderate deviation | Cramer type moderate deviation | STEINS METHOD | TESTS | STATISTICS & PROBABILITY | RANDOM-VARIABLES | Probability | Mathematical Physics | Mathematics

Journal Article

The Annals of statistics, ISSN 0090-5364, 02/2013, Volume 41, Issue 1, pp. 296 - 322

A Cramér moderate deviation theorem for Hotelling’s T^{2}-statistic is proved under a finite (3+\delta)th moment...

62H15 | Cramér moderate deviation | gene selection | 60F10 | FDR | 62E20 | simultaneous hypothesis tests | global tests | brain structure | Hotelling’s T^{2}-statistic

62H15 | Cramér moderate deviation | gene selection | 60F10 | FDR | 62E20 | simultaneous hypothesis tests | global tests | brain structure | Hotelling’s T^{2}-statistic

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 11/2019, Volume 129, Issue 11, pp. 4294 - 4334

We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds...

Large deviations | Cramér’s theorem | Geodesic random walks | Riemannian Brownian motion | Hamilton–Jacobi equation | Non-linear semigroup method | Cramér's theorem | Hamilton-Jacobi equation | Cramer's theorem | STATISTICS & PROBABILITY

Large deviations | Cramér’s theorem | Geodesic random walks | Riemannian Brownian motion | Hamilton–Jacobi equation | Non-linear semigroup method | Cramér's theorem | Hamilton-Jacobi equation | Cramer's theorem | STATISTICS & PROBABILITY

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 10/2012, Volume 7, Issue 5, pp. 919 - 932

For the widely orthant dependent (WOD) structure, this paper mainly investigates the precise large deviations for the partial sums ofWOD and non-identically distributed random variables with dominatedly varying tails...

60F10 | Precise large deviations | 62E20 | Mathematics, general | Mathematics | widely orthant dependent (WOD) | dominatedly varying tails | MATHEMATICS | NEGATIVE DEPENDENCE | CRAMERS CONDITION | ACCOUNT | LAW | INTEGRAL LIMIT THEOREMS | HOLD | SUMS | Random variables | Deviation | Mathematical analysis | China | Sums

60F10 | Precise large deviations | 62E20 | Mathematics, general | Mathematics | widely orthant dependent (WOD) | dominatedly varying tails | MATHEMATICS | NEGATIVE DEPENDENCE | CRAMERS CONDITION | ACCOUNT | LAW | INTEGRAL LIMIT THEOREMS | HOLD | SUMS | Random variables | Deviation | Mathematical analysis | China | Sums

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2007, Volume 35, Issue 2, pp. 673 - 696

Cramér-type large deviations for means of samples from a finite population are established under weak conditions...

Population mean | Approximation | Central limit theorem | Random sampling | Statistical deviations | Mathematical inequalities | Random variables | Asymptotics | Statistics | Moderate deviation | Finite population | Cramér large deviation | BERRY-ESSEEN BOUNDS | INEQUALITIES | EDGEWORTH EXPANSION | moderate deviation | STATISTICS & PROBABILITY | Cramer large deviation | finite population | U-STATISTICS | RANDOM-VARIABLES | 60F05 | 62E20

Population mean | Approximation | Central limit theorem | Random sampling | Statistical deviations | Mathematical inequalities | Random variables | Asymptotics | Statistics | Moderate deviation | Finite population | Cramér large deviation | BERRY-ESSEEN BOUNDS | INEQUALITIES | EDGEWORTH EXPANSION | moderate deviation | STATISTICS & PROBABILITY | Cramer large deviation | finite population | U-STATISTICS | RANDOM-VARIABLES | 60F05 | 62E20

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.