Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process

Stochastic Processes and their Applications

Volumn 103, Issue 2, 2003, Pages 311-349

  Rubenthaler, Sylvain ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Euler scheme; L vy process; Limit theorems; Stochastic differential equations

Indexed keywords

EID: 0037290933     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(02)00191-6     Document Type: Article

References (15)

1. Bally, V., Talay, D., 1996a. The law of the Euler scheme for stochastic differential equations. Probab. Theory Related Fields 104 (1), 43-60.
2. Bally, V., Talay, D., 1996b. The law of the Euler scheme for stochastic differential equations. II. Convergence rate of the density. Monte Carlo Methods Appl. 2 (2), 93-128.
3. Bertoin, J., 1996. Lévy Processes. Cambridge University Press, Cambridge.
4. Jacod, J., 1985. Théorèmes limite pour les processus, École d'été de probabilités de Saint-Flour, XIII-1983, 298-409. Lecture Notes in Mathematics, Vol. 1117. Springer, Berlin-New York.
5. Jacod, J., 1997. On continuous conditional Gaussian martingales and stable convergence in law. Séminaire de Probabilités, XXXI. Lecture Notes in Mathematics, Vol. 1655. Springer, Berlin, 1997, pp. 232-246.
6. Jacod, J., 2001. Sharp estimates for the Euler scheme for Lévy driven stochastic differential equations, mai 2001, Prépublication numéro 656 du Laboratoire de Probabilités et Modéles aléatoires, CNRS-UMR 7599, Université Paris VI et Université Paris VII. http://www.proba.jussieu.fr/ mathdoc/preprints/jj.FriyST01.html.
7. Jacod, J., Protter, P., 1998. Asymptotic error distributions for the Euler method for stochastic differential equations. Ann. Probab. 26 (1), 267-307.
8. Jacod, J., Shiryaev, A.N., 1987. Limit Theorems for Stochastic Processes. Springer, Berlin.
9. 1 de Skorohod. Probab. Theory Related Fields 81, 111-137.
10. Kurtz, T.G., Protter, P., 1990. Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 (3), 1035-1070.
11. Kurtz, T.G., Protter, P., 1991. Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDEs, Stochastic Analysis. Academic Press, Boston, MA, pp. 331-346.
12. Mémin, J., Słominski, L., 1991. Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques, Séminaire de Probabilités, XXV. Lecture Notes in Mathematics, Vol. 1485. Springer, Berlin, pp. 162-177.
13. Protter, P., Talay, D., 1997. The Euler scheme for Lévy Driven stochastic differential equations. Ann. Probab. 25 (1), 393-423.
14. Talay, D., Tubaro, L., 1990. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 (4), 483-509.
15. Słominski, L., 1989. Stability of strong solutions of stochastic differential equations. Stochastic Processes Appl. 31, 173-202.