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Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the…
We propose a modification of a maximum likelihood procedure for tuning parameter values in models, based upon the comparison of their output to field data. Our methodology, which uses polynomial approximations of the sample space to…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
Estimation of stochastic processes evolving in a random environment is of crucial importance for example to predict aircraft trajectories evolving in an unknown atmosphere. For fixed parameter, interacting particle systems are a convenient…
This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
We present a direct parametrization for continuous-time stochastic state-space models that ensures external stability via the stochastic bounded-real lemma. Our formulation facilitates the construction of probabilistic priors that enforce…
Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
Stochastic storage models based on essentially non-Gaussian noise are considered. The stochastic description of physical systems based on stochastic storage models is associated with generalized Poisson (or shot) noise, in which the jump…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…
We present a novel and simple method to numerically calculate Fisher Information Matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function which leads to an…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…