相关论文: Exact Pathwise and Mean--Square Asymptotic Behavio…
In this paper, we are concerned with stochastic Volterra equations with singular kernels and H\"older continuous coefficients. We first establish the well-posedness of these equations by utilising the Yamada-Watanabe approach. Then, we aim…
We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to 0 and $+\infty$.…
The asymptotic shape of randomly growing radial clusters is studied. We pose the problem in terms of the dynamics of stochastic partial differential equations. We concentrate on the properties of the realizations of the stochastic growth…
Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra equation with a fractional kernel. It is well-known that for a standard stochastic differential equation, the discretization error,…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{\"o}lder continuous diffusion coefficients and sufficiently regular kernels. Moreover, we study the…
This paper provide a comprehensive analysis of the finite and long time behavior of continuous-time non-Markovian dynamical systems, with a focus on the forward Stochastic Volterra Integral Equations(SVIEs).We investigate the properties of…
In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $\alpha$-regular Volterra process. Based on the equivalence between neutral retarded stochastic functional differential…
We consider a stochastic Volterra integral equation with regular path-dependent coefficients and a Brownian motion as integrator in a multidimensional setting. Under an imposed absolute continuity condition, the unique solution is a…
We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the…
We study the class of continuous polynomial Volterra processes, which we define as solutions to stochastic Volterra equations driven by a continuous semimartingale with affine drift and quadratic diffusion matrix in the state of the…
Asymptotic properties of solutions of difference equation of the form \[ \Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we…
The asymptotic properties of the memory structure of ARCH($\infty$) equations are investigated. This asymptotic analysis is achieved by expressing the autocovariance function of ARCH($\infty$) equations as the solution of a linear Volterra…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker-Planck equations and show that, much like defective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in…
In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $D^{\alpha}_Cu(t)=Au(t)+f(t)$ on the half line, where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in Caputo's sense,…
In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates…