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Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to…
Quantitatively modeling the trajectories and behavior of pedestrians walking in crowds is an outstanding fundamental challenge deeply connected with the physics of flowing active matter, from a scientific point of view, and having societal…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In robust MDP (RMDP), every action is associated with an uncertainty set of probability distributions, modelling…
Markov Decision Processes (MDPs) offer a fairly generic and powerful framework to discuss the notion of optimal policies for dynamic systems, in particular when the dynamics are stochastic. However, computing the optimal policy of an MDP…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. Using a "penalty method" , an averaging result is obtained when the underlying dynamic is infinitely accelerated. The features of…
We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…
Coarse-grained models of chaotic systems neglect unresolved degrees of freedom, inducing structured model error that limits predictability and distorts long-term statistics. Typical data-driven closures are trained to minimize error over a…
We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location---inter-arrival time Markov…
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…
Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They…
Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…
We explore the statistical and economic importance of restrictions on the dynamics of risk compensation from the perspective of a real-time Bayesian learner who predicts bond excess returns using dynamic term structure models (DTSMs). The…
In this paper, we introduce a time-continuous production model that enables random machine failures, where the failure probability depends historically on the production itself. This bidirectional relationship between historical failure…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
This thesis focuses on the discovery of stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) from noisy and discrete time series. A major challenge is selecting the simplest possible correct model…