Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



Euler approximations of anticipating quasilinear stochastic differential equations

Author: Georgii Shevchenko
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 72 (2005).
Journal: Theor. Probability and Math. Statist. 72 (2006), 167-175
MSC (2000): Primary 60H05; Secondary 60H07, 60H40, 60-08
Published electronically: September 6, 2006
MathSciNet review: 2168146
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain the rate of convergence of Euler type approximations for an anticipating quasilinear stochastic differential equation involving the white noise integral.

References [Enhancements On Off] (What's this?)

  • 1. H. Ahn and A. Kohatsu-Higa, The Euler scheme for anticipating stochastic differential equations, Stoch. Stoch. Rep. 54 (1995), 247-269. MR 1382119 (97b:60098)
  • 2. S. Fang, Théorème limite pour une equation différentielle stochastique anticipative, Stoch. Stoch. Rep. 39 (1992), 95-106. MR 1275359 (95d:60095)
  • 3. H. Holden, B. Øksendal, J. Ubøe, and T. Zhang, Stochastic Partial Differential Equations. A Modeling, White Noise Functional Approach, Birkhäuser, Boston, MA, 1996. MR 1408433 (98f:60124)
  • 4. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992. MR 1214374 (94b:60069)
  • 5. A. Kohatsu-Higa and P. Protter, The Euler scheme for SDE's driven by semimartingales, Stochastic analysis on infinite-dimensional spaces, Pitman Res. Notes Math. Ser., vol. 310, 1994, 141-151. MR 1415665 (97i:60074)
  • 6. D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, New York, 1995. MR 1344217 (96k:60130)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60H05, 60H07, 60H40, 60-08

Retrieve articles in all journals with MSC (2000): 60H05, 60H07, 60H40, 60-08

Additional Information

Georgii Shevchenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

Keywords: Stochastic differential equation, integral with respect to a white noise, Euler approximations, splitting-up method
Received by editor(s): December 17, 2004
Published electronically: September 6, 2006
Additional Notes: Partially supported by grant INTAS YS 03-55-2447.
Article copyright: © Copyright 2006 American Mathematical Society

American Mathematical Society