On the large-deviation principle for the winding angle of a Brownian trajectory around the origin

V. A. Kuznetsov
Theory of Stochastic Processes
Vol.20 (36), no.2, 2015, pp.63-84
In this article we analyse the possibility of obtaining the large-deviation principle for the winding angle of a Brownian motion trajectory around the origin. We prove the weak large-deviation principle and show that the full large-deviation principle cannot hold with any rate function.