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Volterra rough equations

thesis
posted on 13.10.2021, 18:54 by Xiaohua WangXiaohua Wang
We extend the recently developed rough path theory to the case of more rough noise and/or more singular Volterra kernels. It was already observed that the Volterra rough path introduced there did not satisfy any geometric relation, similar to that observed in classical rough path theory. Thus, an extension of the theory to more irregular driving signals requires a deeper understanding of the specific algebraic structure arising in the Volterra rough path. Inspired by the elements of "non-geometric rough paths" developed, we provide a simple description of the Volterra rough path and the controlled Volterra process in terms of rooted trees, and with this description we are able to solve rough Volterra equations driven by more irregular signals.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Samy Tindel

Additional Committee Member 2

Christopher Janjigian

Additional Committee Member 3

Rodrigo Banuelos

Additional Committee Member 4

Fabian A. Harang

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