- A general class of mean field models

Let (En)n≥0 be a sequence of measurable spaces. We consider a collection of transformations Φn+1 : P(En) → P(En+1), n ≥ 0, and we denote by (ηn)n≥0 a sequence of probability measures on En satisfying a nonlinear equation of the following form

ηn+1 = Φn+1 (ηn) (10.1)

The mean field type interacting particle system associated with the Equation (10.1) relies on the fact that the one step mappings can be rewritten in terms of a Markov transport equation

Φn+1 (ηn) = ηnKn+1,ηn (10.2)

for some collection of Markov transitions Kn+1,µ indexed by the time parameter n ≥ 0, and the set of measures µ on the space En.