Related papers: Grand Lebesgue norm estimation for binary random v…

We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…

We say that a random integer variable $X$ is monotone if the modulus of the characteristic function of $X$ is decreasing on $[0,\pi]$. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random…

Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence…

We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for…

We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant.…

We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. The framework we…

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…

A 2022 paper arXiv:2009.10305v4 introduced the notion of true positive and negative skewness for continuous random variables via Fr\'echet $p$-means. In this work, we find novel criteria for true skewness, establish true skewness for the…

This paper develops some general calculus for GGC and Dirichlet process means functionals. It then proceeds via an investigation of positive Linnik random variables, and more generally random variables derived from compositions of a stable…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the…

An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue…

We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…

We consider the $p$-generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $\ell_p^n$-ball in $\mathbb{R}^n$. In this setting the inequality can be improved or reversed up to a respective scalar constant with…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

In this paper, we proved an exact asymptotically sharp upper bound of the $L^p$ Lebesgue Constant (i.e. the $L^p$ norm of Dirichlet kernel) for $p\ge 2$. As an application, we also verified the implication of a new $\infty $-R\'enyi entropy…

In this paper we prove bilinear Strichartz estimates for a solution to the Schr{\"o}dinger map problem whose size is small in the critical Strichartz space $| |\nabla|^{\frac{d - 2}{2}} \psi_{x} |_{L_{t,x}^{\frac{2(d + 2)}{d}}}$. These…

We consider the question as to whether the exponent of a computably presentable Lebesgue space whose dimension is at least 2 must be computable. We show this very natural conjecture is true when the exponent is at least 2 or when the space…

We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…

We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic…