Small-time limit behavior of the probability that a Lévy process stays positive - Knopova, V.P. (Кибернетика и системный анализ, 2016)
In the paper, we find analytically the upper and lower limits (as the time parameter tends to zero) of the probability that the Lévy process staring at 0 stays positive. We confine ourselves to the situation where the real and imaginary parts of the characteristic function are regularly varying at infinity. In this case, we can calculate the bound, and sometimes the exact values of the respective upper and lower limits.