Geometric rough paths on infinite dimensional spaces
| Autor: | Erlend Grong, Torstein Nilssen, Alexander Schmeding |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
22E65
53C17 60H10 60L20 60L50 Applied Mathematics Probability (math.PR) Metric Geometry (math.MG) VDP::Mathematics: 410 Matematikk og Naturvitenskap: 400::Matematikk: 410::Topologi/geometri: 415 [VDP] Matematikk: 410 [VDP] Mathematics: 410 [VDP] Mathematics - Metric Geometry FOS: Mathematics VDP::Matematikk: 410 Matematikk Analysis Mathematics - Probability Mathematics |
| Zdroj: | Journal of Differential Equations |
| Popis: | 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. Comment: 23 pages, v4: major revision |
| Databáze: | OpenAIRE |
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