Related papers: Summation arithmetic functions with asymptotically…
A celebrated result of Hal\'asz describes the asymptotic behavior of the arithmetic mean of an arbitrary multiplicative function with values on the unit disc. We extend this result to multilinear averages of multiplicative functions…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
Let $p$ be a prime number, $k\ge 0$ and $f$ be a class of arithmetic functions satisfying some simple conditions. In this short paper, we study the asymptotical behaviour of summation function $$\psi_{f,k}(x):=\sum_{n\le x}\Lambda…
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. In this paper, the case of specific (non-real analytic) smooth functions is…
In this paper, new asymptotic formulas for sums over zeros of functions from the Selberg class are obtained. These results continue the investigations of Murty $\&$ Perelli \cite{12}, of Murty $\&$ Zaharescu \cite{13}, of Kamiya $\&$ Suzuki…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
We study the growth rate of the summatory function of the M\"obius function in the context of an algebraic curve over a finite field. Our work shows a strong resemblance to its number field counterpart, which was proved by Ng in 2004. We…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
Asymptotic almost automorphy is introduced and studied in the context of some algebras of generalized functions. We also give applications to neutral difference differential systems in the framework of such generalized functions.
We consider integrals over vanishing cycles in the Milnor fibration of an isolated singularity defined by a Newton non-degenerate function. We single out a condition where the leading logarithmic term of the expansion of the integral into a…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
In this paper, we present the asymptotic theory for integrated functions of increments of Brownian local times in space. Specifically, we determine their first-order limit, along with the asymptotic distribution of the fluctuations. Our key…
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…