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This article introduces two techniques for computing the distribution of thefirst passage or absorption time of a drifted Wiener diffusion with Poissonresetting times, in presence of an upper hard wall reflection and a lowerabsorbing barrier. The first method starts with the Pad\'e approximation to theLaplace transform of the first passage time, which is then inverted through thepartial fraction decomposition. The second method, which we call"multiresolution algorithm", is a Monte Carlo technique that exploits theproperties of the Wiener process in order to generate Brownian bridges atincreasing resolution levels. This technique allows to approximate the firstpassage time at any level of accuracy. An intensive numerical study revealsthat the multiresolution algorithm has higher accuracy than standard MonteCarlo, whereas the faster method based on the Pad\'e approximation providessufficient accuracy in specific circumstances only. Besides these two numericalapproximations, this article provides a closed-form expression for the expectedfirst passage time.

Computation of the Distribution of the Absorption Time of the Drifted Diffusion with Stochastic Resetting and Mixed Boundary Conditions