Mathematics Colloquium - Son Luu Nguyen
This event is in the past.
Detroit, MI 48202
Speaker: Professor Son Luu Nguyen, The University of Puerto Rico, Rio Piedras campus
Title: Switching Diffusions with Mean-Field Interactions
Abstract: In this talk we study switching diffusions with mean-field interactions. The motivation stems from regime-switching control systems involving mean-field terms, in which the random switching is modeled as a continuous-time Markov chain. We first obtain a law of large numbers for empirical measures associate with the system. In contrast to the existing literature, the limit measure is not deterministic but random, characterized by the conditional distribution (given the history of the switching process) of the solution to a stochastic McKean-Vlasov differential equation with Markovian switching. Then a stochastic maximum principle for switching diffusions with mean-field interactions is established. Finally, using the maximum principle, optimal controls of linear quadratic Gaussian controls with mean- field interactions for switching diffusions are carried out.