相关论文: Smoothing problem in anticipating scenario

We present embedding procedures for the non-Markovian stochastic Schr\"{o}dinger equations, arising from studies of quantum systems coupled with bath environments. By introducing auxiliary wave functions, it is demonstrated that the…

Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are provided in combining both deterministic sweeping process…

The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…

We study local and global existence and smoothing properties for the initial value problem associated to a higher order nonlinear Schr\"odinger equation with constant coefficients which appears as a model for propagation of pulse in optical…

It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…

We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schr\"odinger equations driven by additive It\^o noise. The class of nonlinearities of interest includes nonlocal…

In this paper we focus on the validity of some fundamental estimates for time-degenerate Schr\"{o}dinger-type operators. On one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison…

We present the Walsh theory of stochastic integrals with respect to martingale measures, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes and some other approaches to…

Starting with the Wigner distribution formulation for beam wave propagation in H\"{o}lder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and…

We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…

We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods,…

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type…

Gaussian smoothing has emerged as an effective technique for reducing the sample complexity of optimal transport. In this paper, we study the two-sample plug-in estimator of the Gaussian-smoothed Wasserstein cost…

We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…

We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…

In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy…

In this article, we give a new proof of the It\^o formula for some integral processes related to the space-time L\'evy white noise introduced in Balan (2015) as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two…

In this paper, we establish ergodic and mixing properties of stochastic 2D Navier-Stokes equations driven by a highly degenerate multiplicative Gaussian noise. The noise could appear in as few as four directions and the intensity of the…

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of…

Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equation; it is sometimes presented as a rule of thumb…