The expected area of the Wiener sausage swept by a disc

Kohei Uchiyama

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arXiv · 1210.6752

The expected area of the Wiener sausage swept by a disc

Kohei Uchiyama

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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,t) remains in a parabolic region. The corresponding result for unconditioned process is also obtained.

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Kohei Uchiyama. 2012-10-25. The expected area of the Wiener sausage swept by a disc. https://arxiv.org/abs/1210.6752

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