Related papers: Hidden Ergodic Ornstein-Uhlenbeck Process and Adap…

We introduce a stochastic approximation method for the solution of an ergodic Kullback-Leibler control problem. A Kullback-Leibler control problem is a Markov decision process on a finite state space in which the control cost is…

Let $\theta>0$. We consider a one-dimensional fractional Ornstein-Uhlenbeck process defined as $dX_t= -\theta\ X_t dt+dB_t,\quad t\geq0,$ where $B$ is a fractional Brownian motion of Hurst parameter $H\in(1/2,1)$. We are interested in the…

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…

This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is…

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic…

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…

We consider a stochastic differential equation with additive fractional noise with Hurst parameter $H>1/2$, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…

The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equations of the process, written in terms of the time…

We consider the problem of approximating the product of $n$ expectations with respect to a common probability distribution $\mu$. Such products routinely arise in statistics as values of the likelihood in latent variable models. Motivated…

Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…

We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter…