Numerical solutions of stochastic functional differential equations. (English) Zbl 1055.65011

Summary: The strong mean square convergence theory is established for the numerical solutions of stochastic functional differential equations under the local Lipschitz condition and the linear growth condition. These two conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here were obtained under quite general conditions.


65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
65L20 Stability and convergence of numerical methods for ordinary differential equations
Full Text: DOI Link


[1] Hu, Numerical solution of stochastic differential systems with memory (2001)
[2] Kloeden, Numerical solutions of stochastic differential equations (1992)
[3] DOI: 10.1137/S0036142901389530 · Zbl 1026.65003
[4] Hale, Introduction to functional differential equations (1993) · Zbl 0787.34002
[5] DOI: 10.1007/BF01203833 · Zbl 0847.60038
[6] DOI: 10.1023/A:1008605221617 · Zbl 0946.60059
[7] DOI: 10.1515/mcma.2001.7.1-2.35 · Zbl 0982.65007
[8] DOI: 10.1016/S0377-0427(00)00475-1 · Zbl 0971.65004
[9] Baker, LMSJ. Comput. Math. 3 pp 315– (2000) · Zbl 0974.65008
[10] DOI: 10.1017/S0962492900002920
[11] Milstein, Numerical integration of stochastic differential equations (1995) · Zbl 0810.65144
[12] DOI: 10.1016/S0377-0427(02)00750-1 · Zbl 1015.65002
[13] Mao, Stochastic differential equations and applications (1997)
[14] Mao, Exponential stability of stochastic differential equations (1994) · Zbl 0806.60044
[15] DOI: 10.1080/01630569408816550 · Zbl 0796.60068
[16] DOI: 10.1016/S0378-4754(00)00224-X
[17] Kolmanovskii, Applied theory of fundamental differential equations (1992)
[18] Hu, Stochastic analysis and related topics V: The Silvri Workshop 38 pp 183– (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.