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arXiv · 2006.06362

Geometric rough paths on infinite dimensional spaces

Erlend Grong·Torstein Nilssen·Alexander Schmeding
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Abstract

Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly geometric $\alpha$-rough paths by signatures of curves of bounded variation, given some tuning of the H\"older parameter. We show that these criteria are satisfied for weakly geometric rough paths on Hilbert spaces. As an application, we obtain Wong-Zakai type result for function space valued martingales using the notion of (unbounded) rough drivers.

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Erlend Grong, Torstein Nilssen, Alexander Schmeding. 2020-06-11. Geometric rough paths on infinite dimensional spaces. https://doi.org/10.1016/j.jde.2022.08.034

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