Related papers: SDE with oblique reflection on domains defined by …
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
In this paper we prove a general approximation result for reflected stochastic differential equations in bounded domains satisfying conditions reorganized by Ren and Wu. Then we show that it includes Wong-Zakai approximation, mollifier…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend…
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…
In this paper, we study reflected backward stochastic difference equations (RBSDEs for short) with finitely many states in discrete time. The general existence and uniqueness result, as well as comparison theorems for the solutions, are…
The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Consider a one-dimensional diffusion process which has state-dependent drift and deviation and is reflected at the origin, which is called a one-side reflected diffusion or simply reflected diffusion. We are particularly interested in the…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…