ON THE FIRST HITTING TIMES FOR ONE-DIMENSIONAL ELLIPTIC DIFFUSIONS

Noufel Frikha (1) , Arturo Kohatsu-Higa (2) , Libo Li (3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Department of Mathematical Sciences, Ritsumeikan Universtiy
3 UNSW - University of New South Wales [Sydney]

In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on the parametrix method that we apply to the associated Markov semigroup. It allows to obtain explicit expressions for the corresponding transition densities and to study its regularity properties up to the boundary under mild assumptions on the coefficients. As a by product, we also provide Gaussian upper estimates for these laws and derive a probabilistic representation that may be useful for the construction of an unbiased Monte Carlo path simulation method, among other applications.

Mots clés: Killed diffusion; parametrix expansion; first hitting time; density estimates

Domaines: Modélisation et simulation; Probabilités [math.PR]

Noufel Frikha, Arturo Kohatsu-Higa, Libo Li. ON THE FIRST HITTING TIMES FOR ONE-DIMENSIONAL ELLIPTIC DIFFUSIONS. 2016. ⟨hal-01373940⟩