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ON THE FIRST HITTING TIMES FOR ONE-DIMENSIONAL ELLIPTIC DIFFUSIONS

By Noufel Frikha, Arturo Kohatsu-Higa and Libo Li

Abstract

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

Topics: Killed diffusion, parametrix expansion, first hitting time, density estimates, [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2016
OAI identifier: oai:HAL:hal-01373940v1
Provided by: Hal-Diderot

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