Related papers: Distributions and Direct Parametrization for Stabl…
By using concrete scenarios, we present and discuss a new concept of probabilistic Self-Stabilization in Distributed Systems.
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
Bayesian methods are increasingly being applied to parameterize mechanistic process models used in environmental prediction and forecasting. In particular, models describing ecosystem dynamics with multiple states that are linear and…
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…
We introduce a new formalism to study nonequilibrium steady-state currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identifying the subspaces in which the system undergoes…
Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the…
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…
Gaussian Process State Space Models (GP-SSM) are a data-driven stochastic model class suitable to represent nonlinear dynamics. They have become increasingly popular in non-parametric modeling approaches since they provide not only a…