Ciesielski’s isomorphism between the space of $\alpha$-Hölder continuous functions and the space of
bounded sequences is used to give an alternative proof of the large deviation principle for Wiener
processes with values in Hilbert space.
We prove that for locally bounded processes, the absence of arbitrage of the first
kind is equivalent to the existence of a dominating local martingale measure. This is related to
results from the theory of filtration enlargements.