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The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts |
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| Authors: | Zbigniew Puchała Tomasz Rolski |
| Affiliation: | 1. Mathematical Institute, University of Wroc?aw, pl.Grunwaldzki 2/4, 50-384, Wroc?aw, Poland 2. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Ba?tycka 5, 44-100, Gliwice, Poland |
| Abstract: | In this note we consider the time of the collision τ for n independent Brownian motions X 1 t ,...,X t n with drifts a 1,...,a n , each starting from x = (x 1,...,x n ), where x 1 < ... < x n . We show the exact asymptotics of ${mathbb{P}}_{bf x}(tau > t) = Ch({bf x})t^{-alpha} {rm e}^{-gamma t}(1 + o(1))$ as t → ∞ and identify C, h(x), α, γ in terms of the drifts. |
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