Related papers: Logarithmic moving averages
We show that effective $2\ell$-multiple correlations imply quantitative $\ell$-multiple pointwise ergodic theorems. The result has a wide class of applications which include subgroup actions on homogeneous spaces, ergodic nilmanifold…
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
We relate transport-entropy inequalities to the study of critical points of functionals defined on the space of probability measures. This approach leads in particular to a new proof of a result by Otto and Villani [43] showing that the…
This is a new proof of the tauberian theorem of complex Laplace transformation for getting a simple proof of the prime numbers theorem $\pi(x) \sim \frac{x}{\log(x)}$ for a largest real $x$.
A generalization of the law of total covariance is presented and proved.
We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type…
We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient…
A formula is derived for the log quantile difference of the temporal aggregation of some types of stable moving average processes, MA(q). The shape of the log quantile difference as a function of the aggregation level is examined and shown…
We show that the moving arithmetic average is closely connected to a Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and which was observed to converge only numerically. Our analysis establishes a rigorous proof of…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We establish new Bombieri-Vinogradov type estimates for a wide class of multiplicative arithmetic functions and derive several applications, including: a new proof of a recent estimate by Drappeau and Topacogullari for arithmetical…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.
The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection…
This paper has two clear motivations: a technical and a practical. The technical motivation unifies in a single and crystal clear formulation a huge family of inequalities that have been produced separately in the last 90 years in different…
In the present paper we obtain sufficient conditions for the existence of equivalent martingale measures for L\'{e}vy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions,…
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
It seems reasonable that a toroid can be thought of approximately as a solenoid bent into a circle. The correspondence of the inductances of these two objects gives an approximation for the natural logarithm in terms of the average of two…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
In one of our former papers {\it Endomorphisms of the measure algebra of commutative hypergroups arXiv:2204.07499 we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra.…