相关论文: Piterbarg's max-discretisation theorem for station…

We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…

Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay…

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…

Ultradiscretization is a limiting procedure transforming a given differential/difference equation into a ultradiscrete equation. Ultradiscrete equations are expressed by addition, subtraction and/or max. The procedure is expected to…

We prove two theorems concerning extreme values of general Gaussian fields. Our first theorem concerns with the concept of multiple peaks. A theorem of Chatterjee states that when a centered Gaussian field admits the so-called…

We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge…

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…

We prove a sharp upper bound for the number of high degree differences in bipartite graphs: let $ (U, V, E)$ be a bipartite graph with $U=\{u_1, u_2, \dots, u_n\}$ and $V=\{v_1, v_2, \dots, v_n\}$; for $n\ge k>\frac{n}{2}$ we show that…

Recently a new class of planar tessellations, named T-tessellations, was introduced. Splits, merges and a third local modification named flip where shown to be sufficient for exploring the space of T-tessellations. Based on these local…

Understanding the relationship between generalization and privacy remains a central challenge in modern machine learning theory, particularly for deep networks trained by variants of differentially private stochastic gradient descent…

We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the…

This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees $ k \ (k…

Graph inference methods have recently attracted a great interest from the scientific community, due to the large value they bring in data interpretation and analysis. However, most of the available state-of-the-art methods focus on…

In this article we study the so-called cut-off phenomenon in the total variation distance when $n\to \infty$ for the family of continuous-time stochastic processes indexed by $n\in \mathbb{N}$, \[ \left( \mathcal{Z}^{(n)}_t=…

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…

The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error…

We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…

The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this…

Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss…