The expected area of the Wiener sausage swept by a disc
Copyright policy )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,t) remains in a parabolic region. The corresponding result for unconditioned process is also obtained.
To appear in Stochastic Processes and their Applications 123 (2013) 191-211
Statistics and Probability, Brownian hitting time, Applied Mathematics, Laplace inversion, Probability (math.PR), Asymptotic expansion, Ramanujan’s function, Modelling and Simulation, Brownian bridge, FOS: Mathematics, Wiener sausage, Mathematics - Probability
Statistics and Probability, Brownian hitting time, Applied Mathematics, Laplace inversion, Probability (math.PR), Asymptotic expansion, Ramanujan’s function, Modelling and Simulation, Brownian bridge, FOS: Mathematics, Wiener sausage, Mathematics - Probability
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