Stochastic processes are probabilistic models which can be used to describe the evolution of systems over time, space or on both. They are widely used to describe phenomena in environmental sciences, engineering, finance and health sciences, just to name few fields. Researchers at IMATI have a long-standing tradition of modelling, statistical inference and applications of stochastic processes, in cooperation with researchers and  practitioners from a wide range of fields.

Markov and point processes (especially Poisson processes) have been widely used as models in the area of reliability of repairable systems, where IMATI researchers are well known for their work on applications, like gas escapes, trains' door failures and bugs detection in software, and on  theoretical aspects, like the recent new notion of signature. Markov models are used to describe the comminution process leading to extraction of precious materials from electrical waste. Dynamic and hidden Markov models are used to describe various aspects of industrial project management, from bidding for the construction of a plant to monitoring ongoing activities with the goal of controlling final costs and delivery times. Stochastic models are used to study the aggregate behaviour of electrical loads and distributed generators, with the aim of supporting the management of the energy distribution networks by the operators of the energy markets.

The study of seismic sequences is another relevant area for which IMATI researchers have been known for years. The randomness of the seismic events naturally leads to the use of stochastic processes. Occurrence of strong earthquakes has been recently described by a multi-rupture model driven by a self-correcting process. Moreover studies have been carried out on the distribution of time between subsequent events. Other studies have led to identify clusters of space-time-magnitude sequences of earthquakes, and the development of hidden Markov models with observations from self-exciting models to identify anomalies in the seismicity rate of regions prone to slow earthquakes and seismic tremors.



Besides the two major areas of interest for IMATI (engineering and earthquakes), stochastic processes are considered in many other contexts, like management of a prototyping service internal to hospitals aimed to the fabrication of personalized prostheses, analysis of terrorist events through self-exciting processes, maps of neonatal mortality through spatial processes and evaluation of management strategies for habitat, climate change and extreme events, besides combination of experts' opinions in Bayesian networks.

The expertise of the IMATI researchers is such that they can use the same model, with minor changes, in different applied fields. Prime examples are the self-exciting processes and the hidden Markov models used in both reliability and earthquakes analysis; the former describe also terrorist activities and the latter are used in project management. The expertise and the interest for applications has lead the stochastic group at IMATI to cooperate with researchers in many fields, at national and international level, with the support of significant grants at local, national and European level.



Raffaele Argiento Antonella Bodini Matteo  Borrotti Ettore Lanzarone Sara Pasquali
Antonio Pievatolo Renata Rotondi Fabrizio Ruggeri Elisa Varini  



R. Argiento, A. Guglielmi, E. Lanzarone, I. Nawajah
A Bayesian framework for describing and predicting the stochastic demand of home care patients. Flex. Serv. Manuf. J. (2015) to appear.

M. Chahkandi, F. Ruggeri, A. Suarez-Llorens
On a Generalized Signature of Repairable Coherent Systems. IEEE Trans. Rel. (2015) to appear.

G. Gilioli, A. Bodini, J. Baumgaertner
Metapopulation modelling and area-wide pest management strategies evaluation.  An application to Pine processionary
Ecol. Model. 260 (2013) 1-10.

A. Pievatolo, F.  Ruggeri, R. Soyer
A Bayesian hidden Markov model for imperfect debugging.
Reliab. Eng. Syst. Safe. 103 (2012) 11-21.

Varini E., Rotondi R. (2015)
Probability distribution of the waiting time in the stress release model: the Gompertz distribution.  Environ. Ecol. Stat. (2015) to appear. 

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