Related papers: The mean value property (corrected version)

This elementary treatment first summarizes extreme values of a Bernoulli random walk on the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric (unbiased) and asymmetric (biased) cases are discussed.…

Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are…

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and…

Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.

In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…

We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left…

The relation between the expectation values computed in the random walk theory, and the heat kernel method for the diffusion equation is explained concretely. The random walk is also realized by simulations and their statistical…

In this note, we consider random walks in the quarter plane with arbitrary big jumps. We announce the extension to that class of models of the analytic approach of [G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter…

A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…

The purpose of this paper is to present some further applications of the general decoupling theory from [B-D1, 2] to certain diophantine issues. In particular, we concider mean value estimates relevant to the Bombieri-Iwaniec approach to…

For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a…

This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…

In this paper, we introduce the degenerate gamma random variables which are connected with the degenerate gamma functions and the degenerate exponential functions, and deduce the expectation and variance of those random variables.

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are…

By developing the entropy theory of random walks on equivalence relations and analyzing the asymptotic geometry of horospheric products we describe the Poisson boundary for random walks on random horospheric products of trees.

In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha; universal…

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

This paper reviews the current state of the art of the mean value theorem due to Thomas M. Flett. We present the results with detailed proofs and provide many new proofs of known results. Moreover, some new observations and yet unpublished…