The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts
Abstract
In this note we consider the time of the collision τ for n independent Brownian motions X1t,...,Xtn with drifts a1,...,an, each starting from x=(x1,...,xn), where x1<...<xn. We show the exact asymptotics of Px(τ>t) = C h(x)t-αe-γ t(1 + o(1)) as t∞ and identify C,h(x),α,γ in terms of the drifts.
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