Barrier crossing of a Levy flight

We consider the barrier crossing in a bistable potential for a random-walk process that is driven by Levy noise of stable index alpha. It is shown that the survival probability decays exponentially, but with a power law dependence T(c)(alpha, D) = C(alpha) D(-mu(alpha)) of the mean escape time on the noise intensity D. Here C is a constant, and the exponent mu varies slowly over a large range of the stable index alpha epsilon [1, 2). Forthe Cauchy case, we explicitly calculate the escape rate.