On the expected volume of the Wiener sausage

• Hamana Yuji

  Department of Mathematics, Kumamoto University

Abstract

We consider the expected volume of the Wiener sausage on the time interval [0,t] associated with a closed ball. Let L(t) be the expected volume minus the volume of the ball. We obtain that L(t) is asymptotically equal to a constant multiple of t^1/2 as t tends to 0 and that it is represented as an absolutely convergent power series of t^1/2 for any t > 0 in the odd dimensional cases. Moreover, the explicit form of L(t) can be given in five and seven dimensional cases.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 62 (4), 1113-1136, 2010

  The Mathematical Society of Japan

Keywords

• Wiener sausage
• power series
• Laplace transform
• Bessel process

Details

• CRID: 1390282680092816384
• NII Article ID: 10027871042
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06241113
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• HANDLE: 2298/33221
• NDL BIB ID: 10859024
• Web Site: https://kumadai.repo.nii.ac.jp/records/29223
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10859024
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed