The expected area of the Wiener sausage swept by a disc

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Uchiyama, Kohei

关键词: Wiener sausage;    Brownian hitting time;    Brownian bridge;    Ramanujan's function;    Asymptotic expansion;    Laplace inversion;   

DOI  :  10.1016/j.spa.2012.09.005

来源: Elsevier

【 摘 要 】

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 [0,1] are computed. It is proved that the leading term of the expectation is given by Ramanujan's function if vertical bar x vertical bar = O(root t). The second term is also given explicitly when vertical bar x vertical bar = o(root t). The corresponding result for unconditioned process is also obtained. (C) 2012 Elsevier B.V. All rights reserved.

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