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We present the analysis of the first passage time problem on a finiteinterval for the generalized Wiener process that is driven by L\'evy stablenoises. The complexity of the first passage time statistics (mean first passagetime, cumulative first passage time distribution) is elucidated together with adiscussion of the proper setup of corresponding boundary conditions thatcorrectly yield the statistics of first passages for these non-Gaussian noises.The validity of the method is tested numerically and compared againstanalytical formulae when the stability index $\alpha$ approaches 2, recoveringin this limit the standard results for the Fokker-Planck dynamics driven byGaussian white noise.Comment: 9 pages, 13 figure

Lévy-Brownian motion on finite intervals: Mean first passage time analysis