Research | Probability and Mathematical Statistics

Research topics

The research activity is directed towards:

• theory and simulation of stochastic processes with applications to biomathematical modeling and queueing systems;
• problems of reliability theory and its applications in stochastic modeling and biocybernetics.

The main research themes include:

1. design of stochastic processes of interest in applied fields, with emphasis on the determination and the analysis of probability laws, such as those of generalized telegraph processes;
2. determination of first-passage-time densities for Gaussian and Markov processes, with special emphasis on diffusion processes, birth-death processes and random walks, by means of analytical and computational techniques;
3. analysis of probabilistic models in various fields related to biomathematics, including models for the dynamics of the neuronal membrane potential by means of Markov and Gaussian processes, models of interaction of several competing population species, models based on jump-diffusion processes.
4. studies of probabilistic and statistical models, stochastic orders, characterizations of random lifetimes, with attention to the setting of new information measures based on entropy and on discrimination functions for random lifetimes;
5. analysis of queueing systems described by Markov processes, both time-varying and subject to catastrophes, and their diffusion approximations.