Related papers: Stochastic recurrence equation with diagonal matri…
We consider systems of stochastic differential equations of the form \[ \d X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) \d Z_t^j\] for $i=1,\dots,d$ with continuous, bounded and non-degenerate coefficients. Here $Z_t^1,\dots,Z_t^d$ are independent…
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…
We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
In this paper, we consider a continuous-time autoregressive fractionally integrated moving average (CARFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian…
In this paper we propose an identification procedure of a sparse graphical model associated to a Gaussian stationary stochastic process. The identification paradigm exploits the approximation of autoregressive processes through reciprocal…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations,…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
We propose an explicit construction of a stationary solution for a stochastic recursion of the form $X\circ\theta=\phi(X)$ on a partially-ordered Polish space, when the monotonicity of $\phi$ is not assumed. Under certain conditions, we…
This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier-Stokes equations in the half line. This is one of the series of papers by the authors on the stability of nonlinear waves…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…