Stochastic Models for Complex Systems

The present project is concerned with the development of Stochastic Models for complex systems whose behavior is uncertain and may be conveniently described in the language of Probability. Stochastic models are nowadays ubiquitous in science, but sometimes they are build under strong assumptions that may limit their use in applications. Here, we focus on the study of stochastic systems in order to relax some usual assumptions such, the Gaussianity in a finite-dimensional system, the Brownian motion in a time-varying context, the lack-of-memory property of a stochastic process (or its related Markovian assumption). For these purposes, the project will develop novel facets in different types of stochastic models that interact with each other. The research targets are organized in six working packages: copula models, reliability models, evolutionary models, random evolution models, semi-Markov models, and neural models. The research team can count on three units (located in Lecce, Napoli and Salerno) with a common interest in stochastic models and a bunch of different methodologies and perspective applications. The research targets will be achieved through a collective effort among the scholars of all the research units.