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An application of fine potential theory to prove a Phragmen Lindelöf theorem

Terry J. Lyons — 1984

Annales de l'institut Fourier

We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset U of the complex plane: if f is analytic on U , bounded near the boundary of U , and the growth of j is at most polynomial then either f is bounded or U { | z | > r } for some positive r and f has a simple pole.

Differential equations driven by rough signals.

Terry J. Lyons — 1998

Revista Matemática Iberoamericana

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...

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