A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss-Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the considered processes
A computational approach to first-passage-time problems for Gauss-Markov processes
NOBILE, Amelia Giuseppina;
2001
Abstract
A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss-Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the considered processesFile in questo prodotto:
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