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Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of…
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques…
A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progression, with the interval as short as possible or the modulus as…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some…
A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.
We prove a conjecture of Broadurst (arXiv:1004.0519v1) on asymptotic expansions of certain polylogarithm type functions related to the Dickman function.
We study the asymptotic behavior of the sums of divisors when the integers are modelled with the Bernoulli random walk; We prealably study the correlation properties of the corresponding system.
Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.
We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data?…
We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…
The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.
Let f be an arithmetic function satisfying certain conditions. In this paper, we give an asymptotic formula for the sum \[\sum_{n_1 n_2 \cdots n_r \leq x} f\left(\left\lfloor \frac{x}{n_1 n_2 \cdots n_r} \right\rfloor\right), \quad r \geq…
We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…
We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…
We review recent results on the existence of asymptotic observables in algebraic QFT. The problem of asymptotic completeness is discussed from this perspective.
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…