The expected area of the Wiener sausage swept by a disc

Kôhei Uchiyama

Stochastic Processes and their Applications, 2013, vol. 123, issue 1, 191-211

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.

Keywords: Wiener sausage; Brownian hitting time; Brownian bridge; Ramanujan’s function; Asymptotic expansion; Laplace inversion (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2012.09.005

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