Related papers: Asymptotically uniform functions: a single hypothe…
We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.
Asymptotic almost automorphy is introduced and studied in the context of some algebras of generalized functions. We also give applications to neutral difference differential systems in the framework of such generalized functions.
The asymptotic behavior, as $T\to\infty$, of some functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,dW_T(s)$, $t\ge0$ is studied. Here $\xi_T(t)$ is the solution to the time-inhomogeneous It\^{o} stochastic differential…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
The purpose of this paper is to show that functions that derivate the two-variable product function and one of the exponential, trigonometric or hyperbolic functions are also standard derivations. The more general problem considered is to…
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…
It is proved that one cannot approximate stably the first derivative of a smooth function given noisy values of this function and a bound on this function and its first derivative. Such an approximation is shown to be possible if an a…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not…
In this paper we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term f on the behavior of the solutions. We prove existence and uniqueness…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
In this article we study a class of delay differential equations with infinite delay in weighted spaces of uniformly continuous functions. We focus on the integrated semigroup formulation of the problem and so doing we provide an spectral…
We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second…
In this article, we study the asymptotics of harmonic functions. A typical method is by proving monotonicity formulas of a version of rescaled Dirichlet energy, and use it to study the renormalized solution -- the Almgren's blowup. However,…
Two theorems on the asymptotic distribution of zeros of sequences of analytic functions are proved. First one relates the asymptotic behavior of zeros to the asymptotic behavior of coefficients. Second theorem establishes a relation between…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
In this paper, we study time-asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of…
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…
This paper is concerned with an abstract dissipative hyperbolic equation with time-dependent coefficient. Under an assumption which ensures that the energy does not decay, this paper provides a condition on the coefficient, which is…