Schilder theorem for the Brownian motion on the diffeomorphism group of the circle (Q557040)

A general class of flows in \(\mathbb{R}^d\) is considered, corresponding to stochastic differential equations (SDE) having (possibly) non-Lipschitz coefficients and driven by infinitely many Brownian motions. First, the authors use the weak convergence approach to large deviations in order to establish a Freidlin-Wentzell theorem for such flows. A Schilder theorem for Brownian motion on the group of homeomorphisms of the circle is then proved, using the fact that such Brownian motion may be presented as the solution to an SDE of the type considered earlier. This involves some extra work, however, since the space of homeomorphisms of \(S^1\) is equipped with its natural topology, which is stronger than the topology associated with uniform convergence of continuous functions.