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Stochastic PDEs and weakly interacting particle systems

Abstract:

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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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Supervisor
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Name:
Engineering and Physical Sciences Research Council
Funder identifier:
http://dx.doi.org/10.13039/501100000266
Grant:
EP/L015811/1
Programme:
EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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