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Thesis

Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian

Abstract:

This thesis is a tale of two halves. The first introduces the space of unparameterised geometric rough paths and develops a notion of Lipschitz function on this space. The second associates an expected signature to the bilaplacian and culminates in an analogue of the Feynman-Kac formula for high-order parabolic partial differential equations.

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Role:
Supervisor

DOI:
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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UUID:
uuid:5805be09-93e5-4f18-b960-732f81f85860
Deposit date:
2019-05-06
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