Abstract: People’s motivation in their private and professional lives are often coupled with reaching certain barriers. Once this barrier is exceeded they will stop doing their activities. The underlying process that needs to hit the barrier can either be deterministic or stochastic. We deal with the stochastic case and discuss results concerning densities of first passage times of strong Markov processes. Apart from a few special cases, analytic solutions are not generally available. We pay particular attention to the Ornstein-Uhlenbeck case, and express the solutions with the help of Integral equations, series and integral representations. The Gaver-Stehfest algorithm for approximating the inverse Laplace transform is studied as well. 

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