相关论文: Stochastic equation on compact groups in discrete …

We propose a discrete functional analysis result suitable for proving compactness in the framework of fully discrete approximations of strongly degenerate parabolic problems. It is based on the original exploitation of a result related to…

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…

We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…

In this paper we establish that the time-harmonic elasticity problem in a half-strip with non-homogeneous Dirichlet conditions on its boundary section and traction-free conditions on its upper and lower boundaries, has a unique weak…

In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from…

In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on…

We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…

This article deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical $\alpha$-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly…

In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…

We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groups are shown to yield isolated groups. We…

It is known that exactness for a discrete group is equivalent to C*-exactness, i.e., the exactness of its reduced C*-algebra. The problem of whether this equivalence holds for general locally compact groups has recently been reduced by Cave…

This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The importance of the notion of compatibility in this definition…

In this article we study mild solutions for the forced, incompressible fractional Navier-Stokes equations. These solutions are classically obtained via a fixed-point argument which relies on suitable estimates for the initial data, the…

This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…

Let $d \ge 2$. In this paper, we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dS_{t}+b(s+t, X_{t})dt, \quad X_{0}=x, \] where $(s,x)\in \mathbb{R}_+ \times \mathbb{R}^{d}$ is the initial starting…

We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…

In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As…

We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between…

We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…

We present collective dynamics of the Cucker-Smale (C-S) ensemble under random communications. As an effective modeling of the C-S ensemble, we introduce a stochastic kinetic C-S equation with a multiplicative white noise. For the proposed…