ABSTRACT
This chapter presents nonlinear Markov processes and their mean field particle interpretations. The usefulness of these models is illustrated by some applications in systemic risk analysis as demonstrated in the description of the Fouque-Sun model and also in fluid mechanics and particle physics. The chapter provides an interpretation of Feynman-Kac measures in terms of jump diffusion processes with killing. The Langevin-McKean-Vlasov model is a stochastic gradient process on R associated with some smooth energy function V, coupled with an attraction or repulsion force around ensemble averages. In nuclear physics, the statistical properties of the spectrum of quantum systems can be analyzed using the nonlinear Dyson equations.
