Related papers: Two laws of large numbers for sublinear expectatio…
Random monotone operators are stochastic versions of maximal monotone operators which play an important role in stochastic nonsmooth optimization. Several stochastic nonsmooth optimization algorithms have been shown to converge to a zero of…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we…
The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this…
In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation…
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…
We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…
Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
Let $\{Y_i,-\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, $\{a_i,-\infty<i<\infty\}$ be an absolutely summable sequence of real numbers. In…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Assessing the stability of a multiple testing procedure under dependence is important but very challenging. Even for multiple testing which among a set of Normal random variables have mean zero, which we refer to as the "Normal means…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…
We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…