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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…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…
In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term,…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…
This paper considers the simultaneous state and unknown input estimation for continuous-discrete stochastic systems. Two types of approaches (with and without modeling of unknown inputs) which can address this issue are investigated. A…
We present a new approach for constructing a data-driven surrogate model and using it for Bayesian parameter estimation in partial differential equation (PDE) models. We first use parameter observations and Gaussian Process regression to…
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by…
We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…
The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space.…
The input-parameter-state estimation capabilities of a novel unscented Kalman filter is examined herein on both linear and nonlinear systems. The unknown input is estimated in two stages within each time step. Firstly, the predicted dynamic…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…
A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…
We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…