A Journal "Theory of Probability and Mathematical Statistics"
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970


Archive

About   Editorial Board   Contacts   Template   Publication Ethics   Peer Review Process   Special Issues   History  

Theory of Probability and Mathematical Statistics



Modified Euler scheme for weak approximation of solutions of stochastic differential equations driven by Wiener process

S. V. Bodnarchuk, A. M. Kulik

Download PDF

Abstract: Weak approximation scheme of solutions of stochastic differential equations driven by Wiener processes is considered.

Keywords: Stochastic differential equations, Euler scheme, weak approximation, Hermite polynomials.

Bibliography:
1. I. I. Gihman, A. V. Skorohod, Stochastic Differential Equations , Springer, Berlin, 1972.
2. E. Hille, R. S. Phillips, Functional analisys and semi-groups , American Mathematical Society, Providence, R. I., 1996.
3. P. E. Kloeden, E. Platen, Numerical solution of stochastic differential equations , Springer, Berlin, 1995.
4. G. Maruyama, Continuous Markov processes and stochastic equations , Rendiconti del Circolo
Matematico di Palermo, 4 (1955), 48-90.
5. R. Mikulevicius, E. Platen, Time Discrete Taylor Approximations for Ito Processes with Jump Component , Mathematische Nachrichten, 138 (1988), 93-104.
6. G. N. Milshtein, A Method of Second-Order Accuracy Integration of Stochastic Differential Equations , Theory Probab. Appl., 23 (1978), no. 2, 396-401.
7. E. Platen, Zur zeitdiskreten Approximation von Itoprozessen , Diss.B., IMath, Akad. der Wiss. der DDR, Berlin (1984).
8. E. Platen, W. Wagner, On a Taylor formula for a class of Ito processes , Probab. and Math. Statistics, 3 (1982), no. 1, 37-51.
9. D. Talay, Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications , Lecture Notes in Control and Information Sciences, 61 (1984), 294-313.