Stochastic PDEs and weakly interacting particle systems

Thesis

We study two problems relating to weakly interacting particle systems in the presence of exogenous noise. Part I presents a pathwise regularisation by noise result for McKean–Vlasov equations with singular interaction kernels. Using ideas from the theory of averaged fields and non-linear Young integrals we obtain well-posedness of the McKean–Vlasov systems, particle approximations and mean field convergence.

In Part II we study a family of semi-linear, convection-diffusion SPDEs th...

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Authors: Mayorcas, A

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: ergodic theory; interacting particle systems; stochastic partial differential equations; stochastic analysis; renormalisation; regularisation by noise
• Subjects: Stochastic partial differential equations; Mathematics; Stochastic analysis