Related papers: Statistical distribution of the Stern sequence
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
It was believed that the Mertens function is a simple random walk in the first versions of the article, so its asymptotic behavior obeys the law of the iterated logarithm. In the latest version of the article we show why the asymptotic…
We introduce several classes of pseudorandom sequences which represent a natural extension of classical methods in random number generation. The sequences are obtained from constructions on labeled binary trees, generalizing the well-known…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…
Much is known about asymptotic expansions for asymptotically normal distributions if these distributions are either absolutely continuous or pure lattice distributions. In this paper we begin an investigation of the discrete but non-lattice…
Two concepts of symmetry for the distributions of positive random variables $Y$ are log-symmetry (symmetry of the distribution of $\log Y$) and R-symmetry [7]. In this paper, we characterise the distributions that have both properties,…
A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…
We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
We define a triangular array closely related to Stern's diatomic array and show that for a fixed integer $r\geq 1$, the sum $u_r(n)$ of the $r$th powers of the entries in row $n$ satisfy a linear recurrence with constant coefficients. The…
The Stern poset $\mathcal{S}$ is a graded infinite poset naturally associated to Stern's triangle, which was defined by Stanley analogously to Pascal's triangle. Let $P_n$ denote the interval of $\mathcal{S}$ from the unique element of row…
We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying $SL_2$ symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can…
The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely understood. This paper studies the superiority of symplectic…
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
We report a detailed and systematic study of wave propagation through a stochastic absorbing random medium. Stochastic absorption is modeled by introducing an attenuation constant per unit length $\alpha$ in the free propagation region of…
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density…