A. Alfonsi, On the discretization schemes for the CIR (and Bessel squared) processes, Monte Carlo Methods and Applications, vol.11, issue.4
DOI : 10.1515/156939605777438569

A. N. Borodin and P. Salminen, Handbook of Brownian Motion : Facts and Formulae . Probability and its applications, Birkhäuser, 1996.

A. Berkaoui, M. Bossy, and A. Diop, Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence, ESAIM: Probability and Statistics, vol.12
DOI : 10.1051/ps:2007030

URL : https://hal.archives-ouvertes.fr/inria-00000176

M. Bossy, E. Gobet, and D. Talay, A symmetrized Euler scheme for an efficient approximation of reflected diffusions, J. Appl. Probab, vol.41, issue.3, pp.877-889, 2004.

C. Costantini, B. Pacchiarotti, and F. Sartoretto, Numerical approximation for functionals of reflecting diffusion processes, SIAM J. Appl. Math, vol.58, issue.1, pp.73-102, 1998.

J. Cox, J. E. Ingersoll, and S. A. Ross, A theory of the term structure of the interest rates, Econometrica, p.53, 1985.

G. Deelstra and F. Delbaen, Convergence of discretized stochastic (interest rate) processes with stochastic drift term. Appl. Stochastic Models Data Anal, pp.77-84, 1998.

A. Diop, Sur la discrétisation et le comportementàcomportementà petit bruit d'EDS unidimensionnelles dont les coefficients sontàsontà dérivéessingulì eres, 2003.

T. D. Dreeben and S. B. Pope, Wall-function treatment in pdf methods for turbulent flows, Physics of Fluids, vol.9, issue.9, pp.2692-2703, 1997.
DOI : 10.1063/1.869381

A. Friedman, Stochastic Differential Equations and Applications, 1975.
DOI : 10.1007/978-3-642-11079-5_2

H. Geman and M. Yor, BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES, Mathematical Finance, vol.1, issue.3, pp.349-375, 1993.
DOI : 10.2307/1427477

J. C. Hull and A. White, Pricing Interest-Rate-Derivative Securities, Review of Financial Studies, vol.3, issue.4, pp.573-592, 1990.
DOI : 10.1093/rfs/3.4.573

I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 1988.

D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, 1996.

P. Protter, Stochastic Integration and Differential Equations, 1990.

I. Unité-de-recherche-inria-sophia and . Antipolis, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, 2004.

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-l` es-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex

I. Editeur and . De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399