Cones of Lower Semicontinuous Functions and a Characterisation of Finely Hyperharmonic Functions.
An application of fine potential theory to prove a Phragmen Lindelöf theorem
We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset of the complex plane: if is analytic on , bounded near the boundary of , and the growth of is at most polynomial then either is bounded or for some positive and has a simple pole.
Differential equations driven by rough signals.
This paper aims to provide a systematic approach to the treatment of differential equations of the type dyt = Σi fi(yt) dxt i where the driving signal xt is a rough path. Such equations are very common and occur particularly frequently in probability where the driving signal might be a vector valued Brownian...
Smoothness of Itô maps and diffusion processes on path spaces (I)
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