Asymptotics of the generating function for the volume of the Wiener sausage

Abstract

We consider the generating function exp(λ|C ε (t)|) of the volume of the Wiener sausage C ε (t), which is the ε-neighbourhood of the Wiener path in the time interval [0,t]. For λ<0, the limiting behaviour for t→∞, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For λ>0 it had been investigated by the first author and B. Tóth, but in contrast to the case λ<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and lar Show more