Euler approximations of anticipating quasilinear stochastic differential equations
Author:
Georgiĭ Shevchenko
Translated by:
V. Semenov
Journal:
Theor. Probability and Math. Statist. 72 (2006), 167-175
MSC (2000):
Primary 60H05; Secondary 60H07, 60H40, 60-08
DOI:
https://doi.org/10.1090/S0094-9000-06-00674-0
Published electronically:
September 6, 2006
MathSciNet review:
2168146
Full-text PDF Free Access
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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
- Hyungsok Ahn and Arturo Kohatsu-Higa, The Euler scheme for anticipating stochastic differential equations, Stochastics Stochastics Rep. 54 (1995), no. 3-4, 247–269. MR 1382119, DOI https://doi.org/10.1080/17442509508834008
- Shizan Fang, Théorème limite pour une équation différentielle stochastique anticipative, Stochastics Stochastics Rep. 39 (1992), no. 2-3, 95–106 (French, with English summary). MR 1275359, DOI https://doi.org/10.1080/17442509208833768
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References
- 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)
- S. Fang, Théorème limite pour une equation différentielle stochastique anticipative, Stoch. Stoch. Rep. 39 (1992), 95–106. MR 1275359 (95d:60095)
- 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)
- P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992. MR 1214374 (94b:60069)
- 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)
- D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer-Verlag, New York, 1995. MR 1344217 (96k:60130)
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Additional Information
Georgiĭ 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
Email:
zhora@univ.kiev.ua
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
