March 2014 Joint densities of first hitting times of a diffusion process through two time-dependent boundaries
Laura Sacerdote, Ottavia Telve, Cristina Zucca
Author Affiliations +
Adv. in Appl. Probab. 46(1): 186-202 (March 2014). DOI: 10.1239/aap/1396360109


Consider a one-dimensional diffusion process on the diffusion interval I originated in x0I. Let a(t) and b(t) be two continuous functions of t, t > t0, with bounded derivatives, a(t) < b(t), and a(t), b(t) ∈ I, for all t > t0. We study the joint distribution of the two random variables Ta and Tb, the first hitting times of the diffusion process through the two boundaries a(t) and b(t), respectively. We express the joint distribution of Ta and Tb in terms of P(Ta < t, Ta < Tb) and P(Tb < t, Ta > Tb), and we determine a system of integral equations verified by these last probabilities. We propose a numerical algorithm to solve this system and we prove its convergence properties. Examples and modeling motivation for this study are also discussed.


Download Citation

Laura Sacerdote. Ottavia Telve. Cristina Zucca. "Joint densities of first hitting times of a diffusion process through two time-dependent boundaries." Adv. in Appl. Probab. 46 (1) 186 - 202, March 2014.


Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 1304.60086
MathSciNet: MR3189054
Digital Object Identifier: 10.1239/aap/1396360109

Primary: 60G40 , 60J60
Secondary: 60J70 , 65R20

Keywords: Brownian motion , copula , diffusion process , First hitting time , Ornstein-Uhlenbeck process

Rights: Copyright © 2014 Applied Probability Trust


This article is only available to subscribers.
It is not available for individual sale.

Vol.46 • No. 1 • March 2014
Back to Top