Self-Normalized Moderate Deviations for Degenerate U-Statistics [PDF]
EntropyIn 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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Sharp Second-Order Pointwise Asymptotics for Lossless Compression with Side Information [PDF]
Entropy, 2020 The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder.
Lampros Gavalakis, Ioannis Kontoyiannis
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A characterization of Chover-type law of iterated logarithm. [PDF]
Springerplus, 2014 Let $0 < \alpha \leq 2$ and $- \infty < \beta < \infty$. Let $\{X_{n}; n \geq 1 \}$ be a sequence of independent copies of a real-valued random variable $X$ and set $S_{n} = X_{1} + \cdots + X_{n}, ~n \geq 1$.
Li D, Chen P.
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A general law of iterated logarithm
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1985 We show that the law of iterated logarithm holds for a sequence of independent random variables \((X_ n)\) provided \[ (i)\quad\sum^{\infty}_{n=1}(s^ 2_ n2\log_ 2s^ 2_ n)^{- p/2}E(| X_ n|^ p)
R. Wittmann
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A Law of Iterated Logarithm for Multi-Agent Reinforcement Learning [PDF]
International Conference on Intelligent Cloud Computing, 2021 In Multi-Agent Reinforcement Learning (MARL), multiple agents interact with a common environment, as also with each other, for solving a shared problem in sequential decision-making.
Gugan Thoppe, Bhumesh Kumar
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Capacity of the range of random walk: The law of the iterated logarithm [PDF]
Annals of Probability, 2022 We establish both the $\limsup$ and the $\liminf$ law of the iterated logarithm (LIL), for the capacity of the range of a simple random walk in any dimension $d\ge 3$.
A. Dembo, Izumi Okada
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A note on the cluster set of the law of the iterated logarithm under sub-linear expectations [PDF]
Probability, Uncertainty and Quantitative Risk, 2022 In this note, we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space.
Li-Xin Zhang
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Small deviations and Chung’s law of iterated logarithm for a hypoelliptic Brownian motion on the Heisenberg group [PDF]
Transactions of the American Mathematical Society. Series B, 2020 A small ball problem and Chung’s law of iterated logarithm for a hypoelliptic Brownian motion in Heisenberg group are proven. In addition, bounds on the limit in Chung’s law are established.
M. Carfagnini, M. Gordina
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Laws of the iterated logarithm for nonparametric sequential density estimators [PDF]
Journal of Statistical Theory and Applications (JSTA), 2013 In this note, we establish a law of iterated logarithm for a triangular array of a random number of independent random variables and apply it to obtain laws of iterated logarithm for the sequential nonparametric density estimators.
Karima Lagha, Smail Adjabi
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Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields [PDF]
Bernoulli, 2021 We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local ...
C. Lee, Yimin Xiao
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