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Stochastic Processes and their Applications, ISSN 0304-4149, 12/2016, Volume 126, Issue 12, pp. 3854 - 3864
In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If f(t0)>0, f′(t0)<0, and f... 
Strassen | Grenander | Monotone density | Limsup | Liminf | Law of iterated logarithm | Limit set | Switching | Strong invariance theorem | Local empirical process | FUNCTIONAL LAWS | BROWNIAN-MOTION | STATISTICS & PROBABILITY | DENSITY | switching | law of iterated logarithm | local empirical process | strong invariance theorem | liminf | limsup | monotone density | limit set
Journal Article
Acta mathematica Hungarica, ISSN 1588-2632, 2007, Volume 118, Issue 1-2, pp. 155 - 170
It is proved that two types of discrepancies of the sequence {θ n x} obey the law of the iterated logarithm with the same constant... 
primary 10K30 | discrepancies | law of the iterated logarithm | lacunary series | secondary 10K05 | 42A55 | Mathematics, general | Mathematics | 60F15 | Lacunary series | Discrepancies | Law of the iterated logarithm | MATHEMATICS | RIESZ-RAIKOV SUMS | SIGMA-F(NKX) | CENTRAL-LIMIT-THEOREM | ASYMPTOTIC-BEHAVIOR
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 6/2019, Volume 32, Issue 2, pp. 721 - 736
Journal Article
Bernoulli, ISSN 1350-7265, 11/2017, Volume 23, Issue 4A, pp. 2330 - 2379
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2016, Volume 59, Issue 12, pp. 2503 - 2526
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 17
.... In this paper, by the Kolmogorov type maximal inequality and Stein’s method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions... 
Stein’s method | law of the iterated logarithm | Analysis | Mathematics, general | Beveridge and Nelson decomposition | Mathematics | linear process | Applications of Mathematics | LNQD sequence | COMPLETE CONVERGENCE | STATIONARY LINEAR-PROCESSES | MATHEMATICS, APPLIED | INEQUALITIES | DEPENDENT RANDOM-VARIABLES | WEIGHTED SUMS | MATHEMATICS | PRODUCTS | Stein's method | ASSOCIATION | CENTRAL-LIMIT-THEOREM | Theorems | Queuing theory | Random variables | Research
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 6/2015, Volume 28, Issue 2, pp. 721 - 725
...J Theor Probab (2015) 28:721–725 DOI 10.1007/s10959-013-0481-4 The Limit Law of the Iterated Logarithm Xia Chen Received: 1 January 2013 / Revised: 8 February... 
Brownian motion | The limit law of the iterated logarithm | 60G10 | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Ornstein–Uhlenbeck process | 60G15 | 60F15 | STATISTICS & PROBABILITY | Ornstein-Uhlenbeck process
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 3/2018, Volume 31, Issue 1, pp. 579 - 597
...J Theor Probab (2018) 31:579–597 https://doi.org/10.1007/s10959-016-0710-8 An Erdös–Révész Type Law of the Iterated Logarithm for Order Statistics... 
Law of the iterated logarithm | Secondary: 60G22 | Probability Theory and Stochastic Processes | 60G70 | Mathematics | Extremes of Gaussian processes | Order statistics process | Statistics, general | Primary: 60F15 | Gaussian processes
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 08/2015, Volume 51, Issue 3, pp. 1124 - 1130
We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales... 
Quantum martingales | Noncommutative martingales | Exponential inequality | Law of the iterated logarithm | STATISTICS & PROBABILITY | 46L53 | 60F15
Journal Article
Asymptotic Analysis, ISSN 0921-7134, 03/2016, Volume 97, Issue 1-2, pp. 91 - 112
The law of the iterated logarithm for some Markov operators, which converge exponentially to the invariant measure, is established... 
law of the iterated logarithm | Markov operators | MATHEMATICS, APPLIED | CONVERGENCE | CHAINS | DIVISION | Mathematics - Probability
Journal Article
Journal of theoretical probability, ISSN 1572-9230, 2014, Volume 29, Issue 1, pp. 32 - 47
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 12/2018, Volume 31, Issue 4, pp. 2366 - 2375
...) for the largest eigenvalue of a GUE matrix recently put forward by E. Paquette and O. Zeitouni. The proof relies on sharp tail bounds and superadditivity, close to the standard law of the iterated logarithm... 
Tracy–Widom distribution | Law of the iterated logarithm | Directed last passage percolation | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Statistics, general | Tail inequalities | 60F15 | STATISTICS & PROBABILITY | Tracy-Widom distribution
Journal Article
by Qi, HS and Yan, LT
JOURNAL OF INEQUALITIES AND APPLICATIONS, ISSN 1029-242X, 04/2018, Volume 2018, Issue 1, pp. 1 - 18
.... In this paper, we give a local law of the iterated logarithm of the form lim sup(s down arrow 0) vertical bar S-t+S(H) - S-t(H)vertical bar/S-H root 2 log... 
MATHEMATICS | MATHEMATICS, APPLIED | LIMIT-THEOREMS | Phi-variation | Iterated logarithm | SYSTEMS | TIME | Sub-fractional Brownian motion | PATH PROPERTIES | Brownian movements | Theorems | 60G22 | Φ-variation | Research | 60F17 | 60G15
Journal Article
Journal of applied probability, ISSN 0021-9002, 12/2012, Volume 49, Issue 4, pp. 978 - 989
...–Uhlenbeck process with linear drift, such as the law of the iterated logarithm (LIL) and Berry–Esseen bounds. As an application of the Berry... 
Maximum likelihood estimator | Precise rate | Ornstein-Uhlenbeck process | Berry-Esseen bound | Law of the iterated logarithm | maximum likelihood estimator | law of the iterated logarithm | 62N02 | 60G50 | Ornstein--Uhlenbeck process | Berry--Esseen bound | precise rate | 60F15
Journal Article
SpringerPlus, ISSN 2193-1801, 12/2014, Volume 3, Issue 1, pp. 1 - 7
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2010, Volume 366, Issue 2, pp. 435 - 443
In this paper, a Chover-type law of the k-iterated logarithm is established for over(ρ, ̃)-mixing sequences of identically distributed random variables... 
Law of the k-iterated logarithm | over(ρ, ̃)-Mixing sequence of random variables | Domain of attraction
Journal Article
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