Stochastic Models for Complex Systems

Project 2019-2023 by Italian MIUR

PRIN 2017

The research targets will be achieved through a collective effort among the scholars of the three units. In relationship with the previously described project targets, Salerno research unit will mainly develop the following specific sub-tasks:

WP2: To investigate the role of information measures on the relevant characteristics of coherent systems. Specifically, we aim to construct new information indices that take into account not only the mean information content of the system random lifetime, but also the variability of such information content in suitable ensembles of systems. This will provide new criteria to assess the reliability of engineering system formed by several components, also with the aim of improving the ageing properties of the involved systems. The research will include also the extension of the Gini-type index to the multidimensional case, in collaboration with Napoli unit.

WP3: Evolutionary models stemmed from the simplest exponential curve are based on constraints and factors that take into account environmental factors and resources. Along the lines drawn in recent researches, we aim to construct a new growth model that is similar to the Gompertz law and the Korf model, but is governed by fractional derivatives. The expected results include the analysis of the relative growth rate and the construction of suitable birth-death processes whose mean evolves as the deterministic model. We aim to validate the models statistically, and to apply them to a suitable dataset on the waste collection in Campania region.

WP4: In the same spirit of previous investigations, we propose to analyze new variants of the telegraph process and to apply the new results to evolution problems of alternating behavior. Specifically, we aim to obtain the probability distribution of the telegraph process in the presence of two alternating boundaries, and to study the relevant properties of these processes. Moreover, multivariate generalizations, like the Rayleigh-type composition of telegraph processes, are considered as well.

WP6: Diffusion processes and Gauss-Markov processes are often used to describe the dynamics of neuronal models. Here, we extend previous results, by constructing simulation procedures for neuronal networks, in order to simulate the sample paths of multidimensional Gauss-Markov processes in the presence of suitable time-dependent reflecting boundaries. The related computations will be compared with the similar analysis performed by the Napoli Unit. This will allow to come to an overall validation of the results thus obtained, and to study complex behaviors of the firing activity of interacting neuronal units.

Salerno Unit Components

Marco Capaldo

Marco Capaldo is a Ph.D. student in Mathematics at the University of Salerno. His research activity is devoted to the study of problems in systems reliability theory and related information measures. Moreover, he focuses on the role of some mathematical tools, such as copulas, distortion functions and stochastic orders, for the analysis of random lifetimes.

Antonio Di Crescenzo

Antonio Di Crescenzo is Full Professor in Probability and Mathematical Statistics at the University of Salerno. His research interests include the theory and simulation of stochastic processes with applications to biomathematics and queuing systems. He has also devoted himself to studying problems in the field of reliability theory also with the aim of providing applications in other fields, such as biocybernetics and stochastic modeling.

Virginia Giorno

Virginia Giorno is Full professor in Computer Science at the University of Salerno. The research interests are turned to the development of general methods for the description and the analysis of complex dynamic systems in evolution. The scientific activity is oriented on the following themes: 1. analysis and comparison of various probabilistic models suitable to describe neuronal systems, as well as adaptive service systems and systems subject to growth in random environment; 2. theoretical studies on Markov and Gaussian processes; 3. design of new efficient algorithms to evaluate first-passage-time densities and their moments in the presence of time-dependent boundaries.

Barbara Martinucci

Barbara Martinucci is Associate Professor of Probability and Mathematical Statistics at the Department of Mathematics of the University of Salerno. Her research interests lie in the general area of stochastic processes with a focus on random evolutions with finite velocity.

Alessandra Meoli

Alessandra Meoli has a Postdoctoral Fellow Position at the Department of Mathematics of University of Salerno. Her research focuses on the application of the fractional paradigm to probability theory, to the description of random motions and random evolutionary dynamics and to reliability theory and survival analysis.

Verdiana Mustaro

Verdiana Mustaro is a PhD student in Mathematics at the University of Salerno. Her current research activity focuses on stochastic modeling of geophysical phenomena through stochastic processes such as Brownian motion and its generalizations.

Amelia Giuseppina Nobile

Amelia Giuseppina Nobile is Full professor in Computer Science at the University of Salerno. Her research interests include the formulation, analysis and comparison of various probabilistic models based on Markov and Gaussian stochastic processes with applications in mathematical biology and in queueing theory, together with the development of efficient numerical algorithms and suitable simulation techniques.

Luca Paolillo

Luca Paolillo is a PhD student in Mathematics at the University of Salerno. His current research interests concern the study of the mathematical properties and applications of entropy and varentropy to continuous random variables.

Paola Paraggio

Paola Paraggio is a PhD student in Mathematics at the University of Salerno. Her research interests are: generalizations of sigmoidal growth models, logistic-type models, fist-passage-time problem, integrated telegraph process, applications of stochastic processes to real fields.

Serena Spina

Serena Spina has a Postdoctoral Fellow Position at the Department of Mathematics of University of Salerno. Her research activity concerns the development and analysis of mathematical models based on continuous and discrete stochastic processes finalized to describe the behaviour of certain dynamical systems.

Fabio Travaglino

Fabio Travaglino is a PhD student in Mathematics at the University of Salerno. His research interests are: probability laws and first passage time problems for processes related to the telegraph process and the Brownian motion, inference for stochastic processes.