The approximate Euler method for Lévy driven stochastic differential equations

Jean Jacod; Thomas G. Kurtz; Sylvie Méléard; Philip Protter

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 3, page 523-558
  • ISSN: 0246-0203

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Jacod, Jean, et al. "The approximate Euler method for Lévy driven stochastic differential equations." Annales de l'I.H.P. Probabilités et statistiques 41.3 (2005): 523-558. <http://eudml.org/doc/77857>.

@article{Jacod2005,
author = {Jacod, Jean, Kurtz, Thomas G., Méléard, Sylvie, Protter, Philip},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Lévy processes; approximation schemes; weak convergence; stability; Euler-Maruyama method; error expansion; Monte Carlo approximation; rate of convergence},
language = {eng},
number = {3},
pages = {523-558},
publisher = {Elsevier},
title = {The approximate Euler method for Lévy driven stochastic differential equations},
url = {http://eudml.org/doc/77857},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Jacod, Jean
AU - Kurtz, Thomas G.
AU - Méléard, Sylvie
AU - Protter, Philip
TI - The approximate Euler method for Lévy driven stochastic differential equations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 3
SP - 523
EP - 558
LA - eng
KW - Lévy processes; approximation schemes; weak convergence; stability; Euler-Maruyama method; error expansion; Monte Carlo approximation; rate of convergence
UR - http://eudml.org/doc/77857
ER -

References

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  2. [2] V. Bally, D. Talay, The law of the Euler scheme for stochastic differential equations (I): convergence rate of the distribution function, Probab. Theory Related Fields104 (1996) 43-60. Zbl0838.60051MR1367666
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  5. [5] J. Jacod, P. Protter, Asymptotic error distributions for the Euler method for stochastic differential equations, Ann. Probab.26 (1998) 267-307. Zbl0937.60060MR1617049
  6. [6] J. Jacod, The Euler scheme for Lévy driven stochastic differential equations, Prépublication LPMS 711, 2002. 
  7. [7] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Heidelberg, 2003. Zbl0635.60021MR1943877
  8. [8] A. Kohatsu-Higa, N. Yoshida, On the simulation of some functionals of solutions of Lévy driven sde's, Preprint, 2001. 
  9. [9] T.G. Kurtz, P. Protter, Wong–Zakai corrections, random evolutions, and simulation schemes for SDEs, in: Mayer-Wolf E., Merzbach E., Shwartz A. (Eds.), Stochastic Analysis, Academic Press, Boston, MA, 1991, pp. 331-346. Zbl0762.60047MR1119837
  10. [10] T.G. Kurtz, P. Protter, Weak error estimates for simulation schemes for SDEs, 1999. 
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  12. [12] P. Protter, D. Talay, The Euler scheme for Lévy driven stochastic differential equations, Ann. Probab.25 (1997) 393-423. Zbl0876.60030MR1428514
  13. [13] J. Rosiński, Series representations of Lévy processes from the perspective of point processes, in: Barndorff-Nielsen O.E., Mikosch T., Resnick S.I. (Eds.), Lévy Processes – Theory and Applications, Birkhäuser, Boston, 2001, pp. 401-415. Zbl0985.60048MR1833707
  14. [14] S. Rubenthaler, Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process, Stochastic Process. Appl.103 (2003) 311-349. Zbl1075.60526MR1950769
  15. [15] L. Słominski, Stability of strong solutions of stochastic differential equations, Stochastic Process. Appl.31 (1989) 173-202. Zbl0673.60065
  16. [16] D. Talay, L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Anal. Appl.8 (1990) 94-120. Zbl0718.60058MR1091544

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