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

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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)

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.

Suggested Citation

  • G. D’Onofrio & E. Pirozzi, 2019. "Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 735-752, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-018-9617-4
    DOI: 10.1007/s11009-018-9617-4
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    References listed on IDEAS

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    1. Hieber, Peter & Scherer, Matthias, 2012. "A note on first-passage times of continuously time-changed Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 165-172.
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