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The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary

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  • Zhao, Zhenwen
  • Xi, Yuejuan

Abstract

This paper studies the first passage times of a (reflected) Brownian motion with broken drift over a random boundary. The time-dependent Meyer–Tanaka formula allows us to obtain the formulas on the joint Laplace transform of the hitting time and hitting position. This paper extends the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry et al. (2004).

Suggested Citation

  • Zhao, Zhenwen & Xi, Yuejuan, 2021. "The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary," Statistics & Probability Letters, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:stapro:v:171:y:2021:i:c:s016771522100002x
    DOI: 10.1016/j.spl.2021.109040
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    References listed on IDEAS

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    1. Su, Fei & Chan, Kung-Sik, 2015. "Quasi-likelihood estimation of a threshold diffusion process," Journal of Econometrics, Elsevier, vol. 189(2), pages 473-484.
    2. Yu, Ting-Hung & Tsai, Henghsiu & Rachinger, Heiko, 2020. "Approximate maximum likelihood estimation of a threshold diffusion process," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    3. Zhang, Tu-Sheng, 1994. "On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 135-147, March.
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