Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes

G. D’Onofrio () and E. Pirozzi ()
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G. D’Onofrio: Institute of Physiology of the Czech Academy of Sciences
E. Pirozzi: Università degli Studi di Napoli Federico II

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 3, 735-752

Abstract: 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.

Keywords: First passage time problem; Ornstein-Uhlenbeck process; Time-dependent boundaries; Gauss-Markov processes; 60G15; 60J70; 60J60 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-018-9617-4

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