Related papers: Functional limit theorems for linear processes wit…
For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.
We study the real, bounded-variables process (X_n) defined by a k-term recurrence relation X_{n+k} ={\phi}(X_n, ... , X_{n+k-1}). We prove the decay of correlations, mainly under purely analytic hypotheses concerning the function {\phi} and…
Many aspects of the asymptotics of Plancherel distributed partitions have been studied in the past fifty years, in particular the limit shape, the distribution of the longest rows, connections with random matrix theory and characters of the…
In this paper, we study the asymptotic behavior of sums of functions of the increments of a given semimartingale, taken along a regular grid whose mesh goes to 0. The function of the $i$th increment may depend on the current time, and also…
Heavy-tailed random samples, as well as their sum or average, are encountered in a number of signal processing applications in radar, communications, finance, and natural sciences. Modeling such data through the Pareto distribution is…
The lower and upper bounds are found for the leading term of summatory totient function $\sum_{k\leq N}k^u\phi^v(k)$ in various ranges of $u\in{\mathbb R}$ and $v\in{\mathbb Z}$.
We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to detect realizability…
The nonlinear signal processing has achieved a rapid process in the recent years. A family of nonlinear Fourier bases, as a typical family of mono-component signals, has been constructed and applied to signal processing. In this paper, the…
Let $ p_n(x) $ be a random polynomial of degree $n$ and $\{Z^{(n)}_j\}_{j=1}^n$ and $\{X^{n, k}_j\}_{j=1}^{n-k}, k<n$, be the zeros of $p_n$ and $p_n^{(k)}$, the $k$th derivative of $p_n$, respectively. We show that if the linear statistics…
We consider an exploration algorithm where at each step, a random number of items become active while related items get explored. Given an initial number of items $N$ growing to infinity and building on a strong homogeneity assumption, we…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
We consider the summatory function of the totient function after applications of a suitable smoothing operator and study the limiting behavior of the associated error term. Under several conditional assumptions, we show that the smoothed…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the non-singlet part of the $e^+e^-$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sum rule of the polarized…
Suppose that $(Z_n)_{n\geq0}$ is a supercritical branching process in independent and identically distributed random environment. The right tail function of the scaled growth rate for $(Z_n)_{n\geq0}$ is studied. The upper bounds for…
A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to…
We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…
The Marcinkiewicz Strong Law, $\displaystyle\lim_{n\to\infty}\frac{1}{n^{\frac1p}}\sum_{k=1}^n (D_{k}- D)=0$ a.s. with $p\in(1,2)$, is studied for outer products $D_k=X_k\overline{X}_k^T$, where $\{X_k\},\{\overline{X}_k\}$ are both…
This paper considers an $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multivariable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions, where each function output…