The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts

Details The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts

2007-04-02

arxiv.org/abs/0704.0215v1

Probab. Theor. Relat. Field., Vol. 142, No. 3-4, pp. 595-617, (2008)

Mathematics

Probability

20 pages

Scientific paper

10.1007/s00440-007-0116-8

In this note we consider the time of the collision $\tau$ 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 $x_1<...$P_x(\tau>t) = C h(x)t^{-\alpha}e^{-\gamma t}(1 + o(1))$ as $t\to\infty$ and
identify $C,h(x),\alpha,\gamma$ in terms of the drifts.

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