The expected area of the Wiener sausage swept by a disc

2012/10/25 by Kôhei Uchiyama, Uchiyama, Kohei
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1210.6752

openalex publication_date 2012/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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