# Singular paths spaces and applications

20 Aug 2020 Bellingeri Carlo Friz Peter K. Gerencsér Máté

Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path setting this allows us to leverage on existing SLE Besov estimates to see that SLE traces takes values in a singular H\"older space, which quantifies a well-known boundary effect in the regime $\kappa < 1$... (read more)

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