Free Access
Issue |
ESAIM: PS
Volume 15, 2011
|
|
---|---|---|
Page(s) | 233 - 248 | |
DOI | https://doi.org/10.1051/ps/2009017 | |
Published online | 05 January 2012 |
- S. Asmussen and J. Rosiński, Approximations of small jumps of Lévy processes with a view towards simulation. J. Appl. Probab. 38 (2001) 482–493. [CrossRef] [MathSciNet] [Google Scholar]
- J.M. Chambers, C.L. Mallows and B.W. Stuck, A method for simulating stable random variables. J. Amer. Statist. Assoc. 71 (1976) 340–344. [Google Scholar]
- U. Einmahl, Extensions of results of Komlos, Major, and Tusnady to the multivariate case. J. Multivariate Anal. 28 (1989) 20–68. [Google Scholar]
- H. Guérin, Solving Landau equation for some soft potentials through a probabilistic approach. Ann. Appl. Probab. 13 (2003) 515–539. [CrossRef] [MathSciNet] [Google Scholar]
- N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, Second edition. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo (1989). [Google Scholar]
- J. Jacod, The Euler scheme for Lévy driven stochastic differential equations: limit theorems. Ann. Probab. 32 (2004) 1830–1872. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jacod, A. Jakubowski and J. Mémin, On asymptotic errors in discretization of processes. Ann. Probab. 31 (2003) 592–608. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jacod, T. Kurtz, S. Méléard and P. Protter, The approximate Euler method for Lévy driven stochastic differential equations. Ann. Inst. H. Poincaré Probab. Statist. 41 (2005) 523–558. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jacod and P. Protter, Asymptotic error distributions for the Euler method for stochastic differential equations. Ann. Probab. 26 (1998) 267–307. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, second edition. Springer-Verlag, Berlin (2003). [Google Scholar]
- J. Komlós, P. Major and G. Tusnády, An approximation of partial sums of independent rvs and the sample df I. Z. Wahrsch. verw. Gebiete 32 (1975) 111–131. [Google Scholar]
- P. Protter and D. Talay, The Euler scheme for Lévy driven stochastic differential equations. Ann. Probab. 25 (1997) 393–423. [CrossRef] [MathSciNet] [Google Scholar]
- E. Rio, Upper bounds for minimal distances in the central limit theorem. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009) 802–817. [CrossRef] [MathSciNet] [Google Scholar]
- S. Rubenthaler, Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process. Stochastic Process. Appl. 103 (2003) 311–349. [CrossRef] [MathSciNet] [Google Scholar]
- S. Rubenthaler and M. Wiktorsson, Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Lévy processes. Stochastic Process. Appl. 108 (2003) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
- H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules. Z. Wahrsch. Verw. Gebiete 46 (1978/79) 67–105. [Google Scholar]
- C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Rat. Mech. Anal. 143 (1998) 273–307. [CrossRef] [MathSciNet] [Google Scholar]
- J.B. Walsh, A stochastic model of neural response. Adv. Appl. Prob. 13 (1981) 231–281. [CrossRef] [Google Scholar]
- A. Yu. Zaitsev, Estimates for the strong approximation in multidimensional central limit theorem. Proceedings of the International Congress of Mathematicians, Vol. III (2002) 107–116. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.