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The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine…
We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the…
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However,…
Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…
The large-scale organization of the world economies is exhibiting increasingly levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover…
This paper introduces a new approach for estimating core inflation indicators based on common factors across a broad range of price indices. Specifically, by utilizing procedures for detecting multiple regimes in high-dimensional factor…
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
We study the so-called pinning model, which describes the behavior of a Markov chain interacting with a distinguished state. The interaction depends on an external source of randomness, called disorder, which can attract or repel the Markov…
A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic…
We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a suitable (empirical) version of the…
This project is going to work with one example of stochastic matrix to understand how Markov chains evolve and how to use them to make faster and better decisions only looking to the present state of the system.
In this paper, we study the controllability and stabilizability properties of the Kolmogorov forward equation of a continuous time Markov chain (CTMC) evolving on a finite state space, using the transition rates as the control parameters.…
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…
A Markovian dichotomic system driven by a deterministic time-periodic force is analyzed in terms of the statistical properties of the switching events between the states. The consideration of the counting process of the switching events…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
In this paper we establish a diffusion limit for a multivariate continuous time Markov chain whose components are indexed by vertices of a finite graph. The components take values in a common finite set of non-negative integers and evolve…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
Substitution Markov chains have been introduced [7] as a new model to describe molecular evolution. In this note, we study the associated Martin boundaries from a probabilistic and topological viewpoint. An example is given that, although…