On the properties of solutions for nonautonomous third-order stochastic differential equation with a constant delay

Abstract

: In this work, complete Lyapunov functionals (LFs) are constructed and used for the established conditions on the nonlinear functions appearing in the main equation, to guarantee stochastically asymptotically stable (SAS), uniformly stochastically bounded (USB) and uniformly exponentially asymptotically stable (UEAS) in probability of solutions to the nonautonomous third-order stochastic differential equation (SDE) with a constant delay as ... x ( t ) + a ( t ) f ( x ( t ) , ˙ x ( t ))¨ x ( t ) + b ( t ) φ (