Abstract
The problem of escape times from a region confined by two time-dependent boundaries is considered for a class of Gauss-Markov processes. Asymptotic approximations of the first exit time probability density functions in case of asymptotically constant and asymptotically periodic boundaries are obtained firstly for the Ornstein-Uhlenbeck process and then extended to the class of Gauss-Markov processes that can be obtained by a specified transformation. Some examples of application to stochastic dynamics and estimations of involved parameters by using numerical approximations are provided.
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Acknowledgements
This work was supported by the Institute of Physiology RVO:67985823, by the Czech Science Foundation project 17-06943S and by Associazione BIOCOMP Napoli.
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D’Onofrio, G., Pirozzi, E. Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes. Methodol Comput Appl Probab 21, 735–752 (2019). https://doi.org/10.1007/s11009-018-9617-4
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DOI: https://doi.org/10.1007/s11009-018-9617-4