相关论文: Smoothing problem in anticipating scenario

A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

The solution of a (stochastic) differential equation (SDE) can be locally approximated by a stochastic expansion, a linear combination of iterated integrals. Quantities of interest, like moments, can then be approximated with the expansion.…

The chaos expansion of a general non-linear function of a Gaussian stationary increment process conditioned on its past realizations is derived. This work combines Wiener chaos expansion approach to study the dynamics of a stochastic system…

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…

The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…

In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…

A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

In this paper, we investigate Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the…

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field…

In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for…

This paper considers the problem of iterative Bayesian smoothing in nonlinear state-space models with additive noise using Gaussian approximations. Iterative methods are known to improve smoothed estimates but are not guaranteed to…

In this note, we establish optimal lower and upper Gaussian bounds for the density of the solution to a class of stochastic integral equations driven by an additive spatially homogeneous Gaussian random field. The proof is based on the…

Since the seminal work of Wiener, the chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations. Yet its complexity for systems subject to the white noise remains significant. The…

Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…

We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general nonlinear multiplicative noise. In the two-dimensional case we…

We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning.…