L. Alili, P. Patie, and J. L. Pedersen, Representations of first hitting time density of an OrnsteinUhlenbeck process, Stochastic Models, vol.21, pp.967-980, 2005.

W. Boyce and R. C. Diprima, Elementary Differential Equations and Boundary Value Problems, 2008.

H. Brézis, Analyse fonctionelle. Collection Mathématiques appliquées pour la maîtrise, 1983.

A. N. Borodin and P. Salminen, Handbook of Brownian motion: facts and formulae. Probability and its applications, 1996.

L. Coutin and M. Pontier, PDE for joint law of the pair of a continuous diffusion and its running maximum, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01591946

L. Coutin, M. Pontier, and W. Ngom, Joint distribution of a lévy process and its running supremum, J. Applied Probability, vol.55, issue.2, pp.488-512, 2018.

F. Delarue, J. Inglis, S. Rubenthaler, and E. Tanré, First hitting times for general non-homogeneous 1d diffusion processes: density estimates in small time, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00870991

A. Ron, A. E. Doney, and . Kyprianou, Overshoots and undershoots of lévy processes, The Annals of Applied Probability, pp.91-106, 2006.

M. Escobar and J. Hernandez, A note on the distribution of multivariate brownian extrema, International Journal of Stochastic Analysis, 2014.

C. W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Springer Series in Synergetics, vol.13, 2004.

H. He, W. Keirstead, and J. Rebholz, Double lookbacks, Mathematical Finance, vol.8, issue.3, pp.201-228, 1998.

M. Jeanblanc, M. Yor, and M. Chesney, Mathematical Methods for Financial Markets, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00426898

I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, 1991.

N. N. Lebedev and R. A. Silverman, Special Functions and Their Applications, 1972.
DOI : 10.1063/1.3047047

W. Ngom, Contributions to the study of default time of a Lévy process in complete observation and in incomplete Observation, 2016.

H. Risken and H. Haken, The Fokker-Planck Equation: Methods of Solution and Applications Second Edition, 1989.

B. D. Sleeman, On parabolic cylinder functions, IMA Journal of Applied Mathematics, vol.4, issue.1, pp.106-112, 1968.

A. Sommerfeld, Sur la théorie analytique de la conduction thermique, Annales mathématiques, vol.45, issue.2, pp.263-277, 1894.