Related papers: The growth of additive processes

In this paper, we study the asymptotic expansion of the flow X(t, x) solution to the nonlinear ODE: X (t, x) = b X(t, x) with X(0, x) = x $\in$ R d , where b is a regular Z dperiodic vector field in R d. More precisely, we provide various…

We consider the problem of absolute continuity for the one-dimensional SDE \[X_t=x+\int_0^ta(X_s) ds+Z_t,\] where $Z$ is a real L\'{e}vy process without Brownian part and $a$ a function of class $\mathcal{C}^1$ with bounded derivative.…

Let $\mathbf{X}=\{X_t\}_{t\geq 0}$ be a L\'evy process in $\mathbb{R}^d$ and $\Omega$ be an open subset of $\mathbb{R}^d$ with finite Lebesgue measure. In this article we consider the quantity $H(t)=\int_{\Omega} \mathbb{P}^x…

Consider a superdiffusion $X$ on $\mathbb R^d$ corresponding to the semilinear operator $\mathcal{A}(u)=Lu+\beta u-ku^2,$ where $L$ is a second order elliptic operator, $\beta(\cdot)$ is in the Kato class and bounded from above, and…

Rosengren and Schlosser introduced notions of ${\it R}_N$-theta functions for the seven types of irreducible reduced affine root systems, ${\it R}_N={\it A}_{N-1}$, ${\it B}_{N}$, ${\it B}^{\vee}_N$, ${\it C}_{N}$, ${\it C}^{\vee}_N$, ${\it…

Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…

Let $\tau$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq…

We consider a class of unstable surface growth models, z_t = -\partial_x J, developing a mound structure of size lambda and displaying a perpetual coarsening process, i.e. an endless increase in time of lambda. The coarsening exponents n,…

In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…

In this paper, we study the growth of solutions to higher-order complex linear differential equations in the unit disc, where the analytic coefficients are of finite ({\alpha},\b{eta},{\gamma})-order. By employing the concepts of…

Existence of long arithmetic progression in sumsets and subset sums has been studied extensively in the field of additive combinatorics. These additive combinatorics results play a central role in the recent progress of fundamental problems…

Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and…

We consider a family of isometric extensions of the full shift on p symbols (for p a prime) parametrized by a probability space. Using Heath-Brown's work on the Artin conjecture, it is shown that for all but two primes p the set of limit…

The purpose of this work is to analyze the blow-up of solutions of the nonlinear parabolic equation \[ u_t-\Delta u=|x|^{\alpha}|u|^{p}+{\mathtt a}(t)\textbf{w}(x) \ \quad\mbox{for } (t,x)\in(0,\infty)\times\mathbb{R}^{N}, \] where $p>1$,…

Let $\{X(\mathbf{t}):\mathbf{t}=(t_1, t_2, \ldots, t_d)\in[0,\infty)^d\}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function $r$ satisfying conditions $r(\mathbf{t})<1$…

In this paper we study the asymptotic behaviour of two relatively new complexity functions defined on infinite words and their relationship to periodicity. Given a factor $u$ of an infinite word $x$, we say $u$ is closed if it is a letter…

Let $A = \{a_{1},a_{2},\dots{}\}$ $(a_{1} < a_{2} < \dots{})$ be an infinite sequence of nonnegative integers, and let $R_{A,2}(n)$ denote the number of solutions of $a_{x}+a_{y}=n$ $(a_{x},a_{y}\in A)$. P. Erd\H{o}s, A. S\'ark\"ozy and V.…

Let $A$ be a set of natural numbers. A set $B$, a set of natural numbers, is said to be an additive complement of the set $A$ if all sufficiently large natural numbers can be represented in the form $x+y$, where $x\in A$ and $y\in B$. This…

Let G=\{G(x),x\in R^1\} be a mean zero Gaussian processes with stationary increments and set \si ^2(|x-y|)= E(G(x)-G(y))^2. Let f be a symmetric function with Ef(\eta)<\ff, where \eta=N(0,1). When \si^2(s) is concave or when \si^2(s)=s^r$,…

Two infinite sequences A and B of non-negative integers are called additive complements, if their sum contains all sufficiently large integers. Let $A(x)$ and $B(x)$ be the counting functions of A and B. In this paper, we extend the results…