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                     Research Activity
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The researches of the Probability group of Torino University consider the following topics in Applied Probability and in computational probability:

  • Development of reliable numerical methods for the solution of Stochastic Differential Equations and for the study of functionals of these solutions ( survival times, first passage times, ...)
  • Development of analytical methods for the solution of Stochastic Differential Equations and for funtionals of these solutions
  • Development of specific methods for the study of first passage times for diffusion processes or jump-diffusion processes through boundaries
  • analytical and simulation methods for the study of tied down processes (bridges)
  • Numerical and analytical methods for the inverse first passage time
  • The study of nonlinear systems in presence of noise via numerical and analytical methods. Stochastic resonance and phenomena induced by the composition of different randomness are part of these researches
  • Jump diffusion processes and their simulation
  • copulae and their use in mathematical modeling
  • Estimation of diffusion parameters for free processes and for processes constrained by boundaries
The use of transformations between diffusion processes, stochastic ordering methods, tied down processes and conditioned processes are typical methods in use for these researches. Information measures are also considered for the study of nonlinear systems with noise.

The group also works on probability problems suggested by modeling in neurosciences and in metrology:

  • The formulation of suitable stochastic models to mimic the coding mechanism in nervous system is a challenging task on which we devote important efforts.The work on this topic is highly interdisciplinary and a continuos exchange of experiences with biologists and neuroscientists is an important characterization of our work. The main goal of these researches is to determine models that can increase our understanding of the neuronal code and could result helpful in the care of illness such as epilepsy or Parkinson disease. Pattern formation mechanisms and synchronization causes are some of the topics investigated to describe features of suitable stochastic models. However these studies result also an important support to recognize new problems in probability theory and have often suggested the development of new methods that result useful also for different applications.

  • The models of atomic clock error are a second topic that have often suggested to us the necessity to develop new reliable probabilistic methods allowing a correct study of the model. These models are in particular the source of researches on reliable algorithms for the solution of nonlinear differential equations and for studies on integrated Brownian motion and on Fractional Brownian motion.