On exit time of stable processes

We study the exit time τ = τ ( 0 , ∞ ) for 1-dimensional strictly stable processes and express its Laplace transform at t α as the Laplace transform of a positive random variable with explicit density. Consequently, τ satisfies some multiplicative convolution relations. For some stable processes, e.g. for the symmetric 2 3 -stable process, explicit formulas for the Laplace transform and the density of τ are obtained as an application.