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The expected area of the Wiener sausage swept by a disc

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  • Uchiyama, Kôhei

Abstract

The expected areas of the Wiener sausages swept by a disc attached to the two-dimensional Brownian Bridge joining the origin to a point x over a time interval [0,t] are computed. It is proved that the leading term of the expectation is given by Ramanujan’s function if |x|=O(t). The second term is also given explicitly when |x|=o(t). The corresponding result for unconditioned process is also obtained.

Suggested Citation

  • Uchiyama, Kôhei, 2013. "The expected area of the Wiener sausage swept by a disc," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 191-211.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:191-211
    DOI: 10.1016/j.spa.2012.09.005
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    1. P. Frevert, 1971. "Note," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 269-270.
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