We consider the Wiener sausage for a Brownian motion up to time $t$associated with a closed ball in even dimensional cases. We obtain theasymptotic expansion of the expected volume of the Wiener sausage for large$t$. The result says that the expansion has many $\log$ terms, which do notappear in odd dimensional cases.
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机译：在偶数尺寸的情况下，我们认为维纳香肠的布朗运动直至$ t $都与一个封闭的球相关。我们获得了$ t $的维也纳香肠预期体积的渐近扩展。结果表明扩展具有许多$ \ log $项，在奇数维情况下不会出现。
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