Related papers: Entropy dissipation via Information Gamma calculus…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyaponuv function, we prove that when the damping is linear, we can find initial…
In this paper we present a data-driven approach for uncertainty propagation. In particular, we consider stochastic differential equations with parametric uncertainty. Solution of the differential equation is approximated using maximum…
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…
We consider a non-standard finite-volume discretization of a strongly non-linear fourth order diffusion equation on the $d$-dimensional cube, for arbitrary $d \geq 1$. The scheme preserves two important structural properties of the…
This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…
We prove a large-data $L^2$-decay estimate for nonlinear dissipative Schr\"odinger equations with attractive-dissipative power nonlinearity. The main difficulty is the lack of sign definiteness of the standard energy when $\Re\lambda<0$,…
We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an…
The paper is concerned with the development of Lyapunov methods for the analysis of equilibrium stability in a dynamical system on the space of probability measures driven by a non-local continuity equation. We derive sufficient conditions…
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time…
We examine entropy production in reduced descriptions of collisionless plasmas. Introducing a closure dependent entropy hierarchy, we show that non-conservative moment closures generate a residual entropy associated with irreversible…
Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on…
We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the…
For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…