Large deviations and Strassen's limit points of Brownian local time processes (Q1365174)

Let \(L(x)\) denote the local time process of a standard Brownian motion \(W\) at the point \(x\in{\mathfrak R}\) and put \(L^*= \sup\{L(x), x\in{\mathfrak R}\}\). It is shown that the probability measures induced by \(L(x)\) and \(L^*\) satisfy generalizations of Schilder's large deviation theorem for \(W\), respectively. Based upon this a certain version of Strassen's functional law of the iterated logarithm is proved for a moving average of Brownian local time. Other applications of the large deviation results are local versions of Strassen's law for Brownian local times.