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Chung’s functional law of the iterated logarithm for the Brownian sheet
In this paper, we investigate functional limit problem for path of a Brownian sheet, Chung’s functional law of the iterated logarithm for a Brownian...
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The Law of the Iterated Logarithm for Spatial Averages of the Stochastic Heat Equation
Let u ( t , x ) be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u (0, x ) = 1 for all x ∈...
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The law of the iterated logarithm for random interval homeomorphisms
A proof of the law of the iterated logarithm for random homeomorphisms of the interval is given.
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The law of the iterated logarithm for two-dimensional stochastic Navier–Stokes equations
We implement the Azencott method to prove the moderate deviation principle for the two-dimensional incompressible stochastic Navier–Stokes equations...
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Diophantine conditions in the law of the iterated logarithm for lacunary systems
It is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables....
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On the Law of the Iterated Logarithm for Sums of Dependent Random Variables
Sufficient conditions are found for the applicability of the generalized law of the iterated logarithm for sums of dependent random variables in the...
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A Law of the Iterated Logarithm for the Empirical Process Based Upon Twice Censored Data
We give a functional law of the iterated logarithm for the increment functions of empirical processes with twice censored data. In this setting, the...
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Quasi Sure Strassen’s Law of the Iterated Logarithm for Increments of FBM in Hölder Norm
AbstractIn this paper, we present functional Strassen’s law of the iterated logarithm for Csörgő–Révész (C–R) increments of a fractional Brownian...
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Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the...
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The Law of the Iterated Logarithm and Probabilities of Moderate Deviations of Sums of Dependent Random Variables
Sufficient conditions are obtained for the applicability of one of the classical forms of the law of iterated logarithm to a sequence of random...
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Lower deviations in β-ensembles and law of iterated logarithm in last passage percolation
For last passage percolation (LPP) on ℤ 2 with exponential passage times, let T n denote the passage time from (1, 1) to ( n,n ). We investigate the law...
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A functional law of the iterated logarithm for multi-class queues with batch arrivals
A functional law of the iterated logarithm (LIL) and its corresponding LIL are established for a multiclass single-server queue with first come first...
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The law of iterated logarithm for the estimations of diffusion-type processes
This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing...
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On the Law of the Iterated Logarithm Without Assumptions About the Existence of Moments
Sufficient conditions are found for the applicability of the generalized law of the iterated logarithm for sums of random variables without...
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Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type
We present sufficient conditions, in terms of the jum** kernels, for two large classes of conservative Markov processes of pure-jump type to be...
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Law of the Iterated Logarithm
For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large...
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Another form of Chover’s law of the iterated logarithm under sub-linear expectations
In this paper, the Chover’s law of the iterated logarithm is established for a sequence of independent and identically distributed random variables...
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The Law of Logarithm for Arrays of Random Variables under Sub-linear Expectations
Under the framework of sub-linear expectation initiated by Peng, motivated by the concept of extended negative dependence, we establish a law of...
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On the Law of Iterated Logarithm for the Maximum Scheme in Ideal Banach Spaces
We obtain asymptotic estimates in the law of iterated logarithm for the extreme values of a sequence of independent random variables in Banach spaces.