A survey of functional laws of the iterated logarithm for self-similar processes [PDF]
, 2007 A process X(t) is self-similar with index H > 0 if the finite-dimensional distributions of X(at) are identical to those of aHX(t) for all a > 0. Consider self-similar processes X(t) that are Gaussian or that can be represented throught Wiener-Itô ...
Czado, Claudia, Taqqu, Murad S.
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Asymptotics for the Moment Convergence of U-Statistics in LIL
Journal of Inequalities and Applications, 2010 Let Un be a U-statistic based on a symmetric kernel h(x,y) and i.i.d. samples {X,Xn;n≥1}. In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of Un are obtained, which extend previous
Ke-Ang Fu
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A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk [PDF]
Journal of Applied Probability, 2015 Let (W n (θ)) n∈ℕ0 be the Biggins martingale associated with a supercritical branching random walk, and denote by W_∞(θ) its limit. Assuming essentially that the martingale (W n (2θ)) n∈ℕ0 is uniformly integrable and that var W 1(θ) is finite, we prove a
A. Iksanov, Z. Kabluchko
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Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm [PDF]
, 2015 We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung’s law of the iterated logarithm are obtained.
Li-Xin Zhang
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On martingale tail sums in affine two-color urn models with multiple drawings [PDF]
, 2016 In two recent works, Kuba and Mahmoud (arXiv:1503.090691 and arXiv:1509.09053) introduced the family of two-color affine balanced Polya urn schemes with multiple drawings. We show that, in large-index urns (urn index between $1/2$ and $1$) and triangular
Kuba, Markus, Sulzbach, Henning
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Laws of the iterated logarithm for symmetric jump processes [PDF]
, 2015 Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for $\beta$
P. Kim, T. Kumagai, Jian Wang
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Representations for Integral Functionals of Kernel Density Estimators
Austrian Journal of Statistics, 2016 We establish a representation as a sum of independent random variables, plus a remainder term, for estimators of integral functionals of the density function, which have a certain simple structure.
David M. Mason
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The law of iterated logarithm for the estimations of diffusion-type processes
Advances in Difference Equations, 2020 This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator ...
Mingzhi Mao, Gang Huang
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Strong limit theorems in the multi-color generalized allocation scheme [PDF]
, 2014 The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers of balls ...
Chuprunov, Alexey, Fazekas, István
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, 2021 We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have Hausdorff dimension $
Stadlbauer, Manuel, Zhang, Xuan
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