Related papers: Large-scale regularity in stochastic homogenizatio…

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…

We consider non-degenerate SDEs with a $\beta$-Holder continuous and bounded drift term and driven by a Levy noise $L$ which is of $\alpha$-stable type. If $\alpha \in [1,2)$ and $\beta \in (1 - \frac{\alpha}{2},1) $ we show pathwise…

We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…

In this paper we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an iid fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is only assumed to be lower semi-continuous and prox-bounded. We combine an adaptive…

In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…

We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction $X+Y \to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent simple…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in $G$-spaces, whether homogeneous or not, provided that a certain $k^{\rm th}$ order jet bundle…

In this paper we prove Liouville type theorem for the stationary Navier-Stokes equations in $\Bbb R^3$ under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth…

We prove a non-mixing property of the flow of the 3D Euler equation which has a local nature: in any neighbourhood of a "typical" steady solution there is a generic set of initial conditions, such that the corresponding Euler flows will…

We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary…

We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…

We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…

A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is…

We study random walks in a balanced, i.i.d. random environment in $\mathbb Z^d$ for $d\geq 3$. We establish improved convergence rates for the homogenization of the Dirichlet problem associated with the corresponding non-divergence form…

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…

We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments,…