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Euler approximations of anticipating quasilinear stochastic differential equations
Author(s):
Georgii
Shevchenko
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
167-175.
MSC (2000):
Primary 60H05;
Secondary 60H07, 60H40, 60-08
Posted:
September 6, 2006
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Abstract:
We obtain the rate of convergence of Euler type approximations for an anticipating quasilinear stochastic differential equation involving the white noise integral.
References:
-
- 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)
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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
Email:
zhora@univ.kiev.ua
DOI:
10.1090/S0094-9000-06-00674-0
PII:
S 0094-9000(06)00674-0
Keywords:
Stochastic differential equation,
integral with respect to a white noise,
Euler approximations,
splitting-up method
Received by editor(s):
17/DEC/2004
Posted:
September 6, 2006
Additional Notes:
Partially supported by grant INTAS YS 03-55-2447.
Copyright of article:
Copyright
2006,
American Mathematical Society
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