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We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
An important question in the field of active matter is whether or not it is possible to predict the phase behavior of these systems. Here, we study the phase coexistence of binary mixtures of torque-free active Brownian particles, for both…
For the standard Quantum Brownian Motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard, one Brownian particle, we show there is at least…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization.…
The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of…
Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into…
We establish well-posedness results for systems of a finite number of stochastic particles driven by independent Brownian motions and subject to a strongly singular drift induced by a Lennard-Jones interaction. In addition to the pairwise…
A symmetrical cubic discrete coupled logistic equation is proposed to model the symbiotic interaction of two isolated species. The coupling depends on the population size of both species and on a positive constant $\lambda$, named the…
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near…
We propose a fully probabilistic formulation of the notion of mechanistic interaction (interaction in some fundamental mechanistic sense) between the effects of putative (possibly continuous) causal factors A and B on a binary outcome…
Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…
Death events commonly arise from complex interactions among interrelated causes, formally classified in reporting practices as underlying and contributing. Leveraging information from death certificates, these interactions can be naturally…