6533b859fe1ef96bd12b6f21
RESEARCH PRODUCT
Geometric rough paths on infinite dimensional spaces
Erlend GrongTorstein NilssenAlexander Schmedingsubject
22E65 53C17 60H10 60L20 60L50Applied MathematicsProbability (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 GeometryFOS: MathematicsVDP::Matematikk: 410MatematikkAnalysisMathematics - ProbabilityMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-01 |