Stochastic models for biomedicine and for reliability in electronic, mechanical and environmental engineering
In the analysis of reliability of multicomponent systems, as in many biomedical and neuroscientifical problems, a quite important aspect concerns the definition and the construction of stochastic models able to describe in a correct and manageable way relations among objects or individuals involved in the study.
For example, in many medical problems the events of interest occur repeatedly over time and the variables describing these multiple events are counts. The numbers of relapses, counted over a certain period of time, are considered as a sign of the disease activity and evolution. In such a situation, stochastic models focused on inter-arrivals times between subsequent events are developed. Such kind of models, used to deeply analyse medical problems, taking in account their real properties, are necessary for the development and the evolution of the medical research.
On the other hand, in the reliability field, the stochastic modelization typically concerns the definition of sizes or measures which can evaluate the stochastic aspects of the problem and their effect on the analysed phenomenon. They can be used, for example, in order to find techniques and instruments to increase the reliability of the system.
In such cases the research of the group is focused on definition of significant measures of the system components to determine, for example, where to concentrate control and maintenance operations.
The mathematical tools mainly used are: stochastic calculus, diffusion processes, stochastic differential equations and mathematical theories of reliability and information.