UC Santa Barbara
Directed chain stochastic differential equations
- Author(s): Detering, Nils
- Fouque, Jean-Pierre
- Ichiba, Tomoyuki
- et al.
Published Web Locationhttps://doi.org/10.1016/j.spa.2019.07.009
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain interaction and (ii) a mean-field interaction. It can be approximated by a limit of finite particle systems, as the number of particles goes to infinity. Due to the local chain interaction, propagation of chaos does not necessarily hold. Furthermore, we exhibit a dichotomy of presence or absence of mean-field interaction, and we discuss the problem of detecting its presence from the observation of a single component process.