Signatures of Gaussian processes and SLE curves
This thesis contains three main results.
The first result states that, outside a slim set associated with a Gaussian process with long time memory, paths can be canonically enhanced to geometric rough paths. This allows us to apply the powerful Universal Limit Theorem in rough path theory to study the quasi-sure properties of the solutions of stochastic differential equations driven by Gaussian processes. The key idea is to use a norm, invented by B. Hambly and T.Lyons, which domina...Expand abstract
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- Awarding institution:
- Oxford University, UK
- Copyright holder:
- Horatio Boedihardjo
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