Related papers: On Asymptotically Orthonormal Sequences
By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them, its explicit expression, the connection with the Euler numbers, its integral representation via the Kontorovich-Lebedev…
Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents sufficient conditions for the asymptotic normality (for $n\to\infty$…
Parseval and equal-norm frames play a fundamental role in frame theory and signal processing. In this work, we prove non-asymptotic concentration bounds showing that random equal-norm frames are nearly Parseval with high probability, and…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
Based on the parallelogram law and isosceles orthogonality, we define a new orthogonal geometric constant. We first discuss some basic properties of this new constant. Next, we consider the relation between the constant and the uniformly…
We consider sequences of biorthogonal polynomials with respect to a Cauchy type convolution kernel and give the weak and ratio asymptotic of the corresponding sequences of biorthogonal polynomials. The construction is intimately related…
Asymptotically safe gravity is based on the idea that the main contribution to the Schwarzschild-like black hole spacetime is due to the value of the gravitational coupling which depends on the distance from the origin and approaches its…
We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13].…
In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
Let $A$ be an $n \times M$ matrix whose rows are orthonormal. Let $A_I$ be a submatrix of $A$ whose column indexes belong to the set $I$. Given $\epsilon >0$ we estimate the smallest cardinality of the set $I$, such that the operator $A_I$…
We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of P\'olya and Szeg\"o, so the error incurred in truncating the series is of the same sign as the next…
We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then the manifold has a canonical…
A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a…
We establish a Bohr-Sommerfeld type condition for quasi-normal modes of a slowly rotating Kerr-de Sitter black hole, providing their full asymptotic description in any strip of fixed width. In particular, we observe a Zeeman-like splitting…
We show that the posterior distribution of parameters in a hidden Markov model with parametric emission distributions and discrete and known state space is asymptotically normal. The main novelty of our proof is that it is based on a…
In this short note we present a far generalization of the following very well-known assertion: assume that we have two orthonormal sequences in a Hilbert space and these sequences are quadratically close to each other. Then if one of these…
We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…