Докладчик: Сергей Бернардович Майорга-Татарин (Sergio Mayorga Tatarin), Baylor University, USA.

Аннотация. The mean-field limit approach in particle systems is a way to reduce a large number of equations about many particles to a single equation in an infinite-dimensional space. The indistinguishability of the particles means that their distribution is represented by a probability measure, so the value function that arises heuristically as the limit of value functions of the control problem in finite dimensions, should presumably satisfy a HJB equation stated in a space of probability measures (the Wasserstein space). I will discuss one rigorous interpretation of this. To this end I will explain the notion of "L-viscosity solution", which allows to circumvent intrinsic difficulties of the Wasserstein space, and then I will present on a recent convergence result, that can be seen as justifying the interpretation. A representation formula for the limiting value function also exists, and is related to the so-called master equation in mean-field games; I will describe these notions and their recent developments.