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Directed chain stochastic differential equations

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  • Detering, Nils
  • Fouque, Jean-Pierre
  • Ichiba, Tomoyuki

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.

Suggested Citation

  • Detering, Nils & Fouque, Jean-Pierre & Ichiba, Tomoyuki, 2020. "Directed chain stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2519-2551.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:2519-2551
    DOI: 10.1016/j.spa.2019.07.009
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    References listed on IDEAS

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    1. Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
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    Cited by:

    1. Lacker, Daniel & Ramanan, Kavita & Wu, Ruoyu, 2021. "Locally interacting diffusions as Markov random fields on path space," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 81-114.

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