New results in stability theory for stochastic functional differential equations (SEDEs) and their applications. (English) Zbl 0811.34062

Ladde, G. S. (ed.) et al., Dynamic systems and applications. Vol. 1. Proceedings of the 1st international conference, held at Morehouse College, Atlanta, GA, USA, May 26-29, 1993. Atlanta, GA: Dynamic Publishers, Inc. 167-171 (1994).
The authors propose a systematic way to construct Lyapunov functionals to prove mean square stability of the trivial solution of a stochastic functional differential equation by decomposing drift and diffusion into a part which only depends on the current state and a part which depends on the past. They provide several examples to show that their approach works.
For the entire collection see [Zbl 0802.00023].


34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K20 Stability theory of functional-differential equations