Keep the particles -- CANCELLED

Status: This talk is in preparation - details may change
Status: This talk has been cancelled

Some of the basic ideas and methodology of what has been called the “bring back the particles” approach to infinite population limits will be described. The approach is perhaps better described as “don’t let the particles get away in the first place” or simply “keep the particles”. In many areas (for example, population biology. statistical physics, queueing), models of large numbers of interacting entities (particles) are considered as the number of particles tends to infinity. Classically, the approach has been to consider the normalized empirical measure determined by the particles, argue that the empirical measure must converge as the size of the system tends to infinity, and then identify the limiting measure as the solution of a PDE or SPDE, a measure-valued stochastic process, etc. “Keep the particles” says that the limit of finite systems as the number of particles goes to infinity should be an infinite system. The classical McKean-Vlasov model will be considered along with a closely related model of asset prices. Time permitting, using the approach to derive filtering equations will be discussed.