Residence time statistics of the random acceleration model

Hermann Joel Ouandji Boutcheng, Thomas Bouetou Bouetou, Theodore W. Burkhardt, Alberto Rosso, Andrea Zoia, Kofane Timoleon Crepin

Published 2016-03-22Version 1

The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the residence time and related properties are nontrivial and not yet completely understood. In this paper we consider the residence time of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments explicitly and support the analytical results with Monte Carlo simulations.