Central Limit Results for Jump-Diffusions with Mean Field Interaction and a Common Factor

Abstract

A system of $N$ weakly interacting particles whose dynamics is given in terms of jump-diffusions with a common factor is considered. The common factor is described through another jump-diffusion and the coefficients of the evolution equation for each particle depend, in addition to its own state value, on the empirical measure of the states of the $N$ particles and the common factor. A Central Limit Theorem, as $N\to \infty$, is established. The limit law is described in terms of a certain Gaussian mixture. An application to models in Mathematical Finance of self-excited correlated defaults is described.

References in corpus (1)

• A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs

Cited by in corpus (1)

• Some Fluctuation Results for Weakly Interacting Multi-type Particle System