Related papers: Statistical Parameter Calibration via the Generali…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Parameter estimation, which represents a classical inverse problem, is often ill-posed as different parameter combinations can yield identical outputs. This non-uniqueness poses a critical barrier to accurate and unique identification. This…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters…
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function,…
The fluctuation-dissipation theorem (FDT) is a simple yet powerful consequence of the first-order differential equation governing the dynamics of systems subject simultaneously to dissipative and stochastic forces. The linear learning…
We present a generalized linear response theory for mixed jump-diffusion models -- combining Gaussian and L\'evy noise interacting with nonlinear dynamics -- by deriving comprehensive response formulas accounting for perturbations to both…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…
Using the initial-value formulation, a dynamic theory for systems evolving according to a Generalized Langevin Equation is developed, providing more restrictive conditions on the existence of equilibrium behavior and its…
We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that by using a general functional decomposition for space-time dependent forcings, we can define elementary susceptibilities…
We develop a unified fluctuation-response theory in the frequency domain for nonequilibrium steady states governed by overdamped Langevin dynamics and Markov jump processes. The relation expresses the power spectrum of general observables…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential…