Báo Cáo Báo cáo hóa học LYAPUNOV FUNCTIONALS CONSTRUCTION FOR STOCHASTIC DIFFERENCE SECOND-KIND VOLTERRA EQU

LYAPUNOV FUNCTIONALS CONSTRUCTION FOR STOCHASTIC DIFFERENCE SECOND-KIND VOLTERRA EQUATIONS WITH CONTINUOUS TIME LEONID SHAIKHET

Received 4 August 2003 The general method of Lyapunov functionals construction which was developed during the last decade for stability investigation of stochastic differential equations with aftereffect and stochastic difference equations is considered. It is shown that after some modification of the basic Lyapunov-type theorem, this method can be successfully used also for stochastic difference Volterra equations with continuous time usable in mathematical models. The theoretical results are illustrated by numerical calculations.

1. Stability theorem Construction of Lyapunov functionals is usually used for investigation of stability of hereditary systems which are described by functional differential equations or Volterra equations and have numerous applications [3, 4, 8, 21]. The general method of Lyapunov functionals construction for stability