Results 11 to 20 of about 1,835 (300)

The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation [PDF]

Entropy, 2021
In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive ...
Wei Liu, Yong Zhang
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The law of the iterated logarithm for LNQD sequences [PDF]

Journal of Inequalities and Applications, 2018
Let { ξ i , i ∈ Z } $\{\xi_{i},i\in{\mathbb{Z}}\}$ be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein’s method, we establish the result of the law of ...
Yong Zhang
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On the law of the iterated logarithm. [PDF]

Proc Natl Acad Sci U S A, 1969
The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so.
Slivka J.
europepmc   +5 more sources

One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions [PDF]

Journal of Mathematics, 2023
The law of the iterated logarithm (LIL), which describes the rate of convergence for a convergent lacunary series, was established by R. Salem and A. Zygmund.
Santosh Ghimire
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The Law of the Iterated Logarithm

Journal of Institute of Science and Technology, 2022
The article begins first with the history and the development of the law of the iterated logarithm, abbreviated LIL. We then discuss the LIL in the context of independent random variables, dyadic martingales, lacunary trigonometric series, and harmonic functions. Finally, we derive a LIL for a sequence of dyadic martingales.
Santosh Ghimire, Hari Bagale Thapa
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A law of the iterated logarithm for Grenander's estimator. [PDF]

Stoch Process Their Appl, 2016
In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0) > 0$, $f'(t_0) < 0$, and $f'$ is continuous in a neighborhood of $t_0$, then \begin{eqnarray*} \limsup_{n\rightarrow \infty} \left ( \frac{n}{2\log \log n} \right )^{1/3} ( \widehat{f}_n (t_0 ) - f(t_0 ...
Dümbgen L, Wellner JA, Wolff M.
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A generalization of Kolmogorov’s law of the iterated logarithm [PDF]

Proceedings of the American Mathematical Society, 1972
A version of the law of the iterated logarithm is proved for sequences of independent random variables which satisfy the central limit theorem in such a way that the convergence of the appropriate moment-generating functions to that of the standard normal distribution occurs at a particular rate.
R. J. Tomkins
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Self-Normalized Moderate Deviations for Degenerate U-Statistics [PDF]

Entropy
In this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h(x,y)=∑l=1∞λlgl(x)gl(y), where λl>0, Egl(X1)=0,
Lin Ge, Hailin Sang, Qi-Man Shao
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Chover-Type Laws of the Iterated Logarithm for Kesten-Spitzer Random Walks in Random Sceneries Belonging to the Domain of Stable Attraction [PDF]

Discrete Dynamics in Nature and Society, 2018
Let X={Xi,i≥1} be a sequence of real valued random variables, S0=0 and Sk=∑i=1kXi  (k≥1). Let σ={σ(x),x∈Z} be a sequence of real valued random variables which are independent of X’s.
Wensheng Wang, Anwei Zhu
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A law of iterated logarithm for the subfractional Brownian motion and an application [PDF]

Journal of Inequalities and Applications, 2018
Let SH={StH,t≥0} $S^{H}=\{S^{H}_{t},t\geq0\}$ be a sub-fractional Brownian motion with Hurst index 00) $(x>0)$ with ΦH(0)=0 $\Phi_{H}(0)=0$.
Hongsheng Qi, Litan Yan
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