2017年3月

A formula for the expected volume of the Wiener sausage with constant drift

FORUM MATHEMATICUM
• Yuji Hamana
• ,
• Hiroyuki Matsumoto

29
2

369

381

DOI
10.1515/forum-2016-0039

WALTER DE GRUYTER GMBH

We consider the Wiener sausage for a Brownian motion with a constant drift up to time t associated with a closed ball. In the two or more dimensional cases, we obtain the explicit form of the expected volume of the Wiener sausage. The result says that it can be represented by the sum of the mean volumes of the multidimensional Wiener sausages without a drift. In addition, we show that the leading term of the expected volume of the Wiener sausage is written as kappa t(1+o[1]) for large t by a constant kappa. The expression for kappa is of a complicated form, but it converges to the known constant as the drift tends to 0.

リンク情報
DOI
https://doi.org/10.1515/forum-2016-0039
Web of Science