ASYMPTOTIC EXPANSION OF THE EXPECTED VOLUME OF THE WIENER SAUSAGE IN EVEN DIMENSIONS

摘要

We consider the Wiener sausage for a Brownian motion up to time t associated with a closed ball in even-dimensional cases. We obtain the asymptotic expansion of the expected volume of the Wiener sausage for large t. The result says that the expansion has many log terms, which do not appear in odd-dimensional cases.