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An inverse first-passage problem for one-dimensional diffusions with random starting point

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  • Abundo, Mario

Abstract

We consider an inverse first-passage time (FPT) problem for a homogeneous one-dimensional diffusion X(t), starting from a random position η. Let S(t) be an assigned boundary, such that P(η≥S(0))=1, and F an assigned distribution function. The problem consists of finding the distribution of η such that the FPT of X(t) below S(t) has distribution F. We obtain some generalizations of the results of Jackson et al., 2009, which refer to the case when X(t) is Brownian motion and S(t) is a straight line across the origin.

Suggested Citation

  • Abundo, Mario, 2012. "An inverse first-passage problem for one-dimensional diffusions with random starting point," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 7-14.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:7-14
    DOI: 10.1016/j.spl.2011.09.005
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    References listed on IDEAS

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    1. Abundo, Mario, 2002. "Some conditional crossing results of Brownian motion over a piecewise-linear boundary," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 131-145, June.
    2. Jackson, Ken & Kreinin, Alexander & Zhang, Wanhe, 2009. "Randomization in the first hitting time problem," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2422-2428, December.
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    Cited by:

    1. Abundo, Mario, 2016. "On the excursions of drifted Brownian motion and the successive passage times of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 176-182.
    2. Abundo, Mario & Pirozzi, Enrica, 2018. "Integrated stationary Ornstein–Uhlenbeck process, and double integral processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 265-275.
    3. Abundo, Mario, 2013. "The double-barrier inverse first-passage problem for Wiener process with random starting point," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 168-176.

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