DIFFUSION HITTING TIMES AND THE BELL-SHAPE

Wissem Jedidi (1, 2) , Thomas Simon (3, 4)

1 KSU - King Saud University [Riyadh]
2 UTM - Université de Tunis El Manar
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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.

Mots clés: Bell-shape; Exponential mixture; Generalized diffusion; Hitting time; Speed measure

Domaines: Probabilités [math.PR]

Wissem Jedidi, Thomas Simon. DIFFUSION HITTING TIMES AND THE BELL-SHAPE. 2015. ⟨hal-01136764⟩