相关论文: Projective Stationary Sets and Strong Reflection P…

Given a domain G, a reflection vector field d(.) on the boundary of G, and drift and dispersion coefficients b(.) and \sigma(.), let L be the usual second-order elliptic operator associated with b(.) and \sigma(.). Under suitable…

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…

In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…

Consider a general nonlinear optimal control problem in finite dimension, with constant state and/or control delays. By the Pontryagin Maximum Principle, any optimal trajectory is the projection of a Pontryagin extremal. We establish that,…

We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n+1} = \sum_{j=1}^n p_n(j) a_j$. Our results extend classical theory in two distinct regimes. First, we prove a…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

We consider a general multivariate affine stochastic recursion and the associated Markov chain on $\mathbb R^{d}$. We assume a natural geometric condition which implies existence of an unbounded stationary solution and we show that the…

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

We consider a particular instance of reflection of shock waves in self-similar compressible flow. We prove that local self-similar regular reflection (RR) cannot always be extended into a global flow. Therefore the detachment criterion is…

The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…

We consider the systems of diffusion-orthogonal polynomials, defined in the work [1] of D. Bakry, S. Orevkov and M. Zani and (particularly) explain why these systems with boundary of maximal possible degree should always come from the…

Interaction of a domain wall with boundaries of a system is studied for a class of stochastic driven particle models. Reflection maps are introduced for the description of this process. We show that, generically, a domain wall reflects…

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…

In a recent work, Blanc, Le Bris, and Lions defined a notion of increment-stationarity for random point sets, which allowed them to prove the existence of a thermodynamic limit for two-body potential energies on such point sets (under the…

We show that every invertible strong mixing transformation on a Lebesgue space has strictly over-recurrent sets. Also, we give an explicit procedure for constructing strong mixing transformations with no under-recurrent sets. This answers…

Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative…

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…

Extending Aanderaa's classical result that $\pi^1_1<\sigma^1_1$, we determine the order between any two patterns of iterated $\Sigma^1_1$- and $\Pi^1_1$-reflection. We show that this \emph{linear reflection order} is a prewellordering of…