The expected area of the Wiener sausage swept by a disc
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.
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Volume (Year): 123 (2013)
Issue (Month): 1 ()
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