The "Classical and Quantum Stochastic Models" group works on the development and mathematical study of models based on classical and quantum probability, integrating various probabilistic, statistical and analytical skills. The models studied are useful for describing and understanding various random phenomena in physics, biology, finance, economics and social sciences. In detail, the main skills and interests of the group are:

Classical stochastic models

• Optimal control in finite and infinite dimensions of Markov and non-Markov, diffusion and pure jump processes; linear and quadratic control, retrograde stochastic equations. Applications to financial modeling.  Satellite site https://www.mate.polimi.it/control/ contact person: Fulvia Confortola
• Construction, theoretical analysis and asymptotic study of stochastic processes for complex systems: Markov processes, spatial models and point processes, random graphs, systems of interacting particles, branching processes.
• Bayesian inference for complex systems (described above).
• Study of stochastic models of information/epidemic diffusion, contagion processes.
• Stochastic nonlinear partial differential equations, regularization for noise and applications to physical models.

Quantum stochastic models

• Development of the theory and applications of dynamics for quantum open systems, general theory of quantum Markov semigroups and their GKLS generators.
• Stochastic Schrödinger equations and quantum stochastic differential equations.
• Development of entropic techniques for the analysis of information and uncertainty in quantum systems, with applications to the emerging field of quantum technologies.

Sito satellite: https://www.mate.polimi.it/qp/
referente: Ameur Dhahri