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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- University of Oxford
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Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian
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