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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Year of publication:	2013
Authors:	Uchiyama, Kôhei
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 123.2013, 1, p. 191-211
Publisher:	Elsevier
Subject:	Wiener sausage \| Brownian hitting time \| Brownian bridge \| Ramanujan’s function \| Asymptotic expansion \| Laplace inversion

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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