Directed chain stochastic differential equations

Nils Detering, Jean-Pierre Fouque and Tomoyuki Ichiba

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 2519-2551

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.

Keywords: Interacting stochastic processes; Stochastic equation with constraints; Law of large numbers; Particle system approximation; Detecting mean-field (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:4:p:2519-2551

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DOI: 10.1016/j.spa.2019.07.009

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