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arXiv · 1805.01962

Directed Chain Stochastic Differential Equations

Nils Detering·Jean-Pierre Fouque·Tomoyuki Ichiba
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Abstract

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.

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Nils Detering, Jean-Pierre Fouque, Tomoyuki Ichiba. 2018-05-04. Directed Chain Stochastic Differential Equations. https://arxiv.org/abs/1805.01962

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