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Diffusion hitting times and the bell-shape

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  • Jedidi, Wissem
  • Simon, Thomas

Abstract

Consider a generalized diffusion on R with speed measure m, in the natural scale. It is known that the conditional hitting times have a unimodal density function. We show that these hitting densities are bell-shaped if and only if m has infinitely many points of increase between the starting point and the hit point. This result can be viewed as a visual corollary to Yamazato’s general factorization for diffusion hitting times.

Suggested Citation

  • Jedidi, Wissem & Simon, Thomas, 2015. "Diffusion hitting times and the bell-shape," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 38-41.
    • Handle: RePEc:eee:stapro:v:102:y:2015:i:c:p:38-41
    DOI: 10.1016/j.spl.2015.03.008
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    References listed on IDEAS

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    1. Barndorff-Nielsen, O. & Blæsild, P. & Halgreen, C., 1978. "First hitting time models for the generalized inverse Gaussian distribution," Stochastic Processes and their Applications, Elsevier, vol. 7(1), pages 49-54, March.
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