Stability of Stochastic Functional Differential Equations

Here we will consider the Itô type SRDE 1.1$$\left. {\begin{array}{*{20}{c}} {dx\left( t \right) = {a_1}\left( {t,{x_t}} \right)dt + {a_2}\left( {t,{x_t}} \right)d\xi \left( t \right),{\kern 1pt} t \geqslant {t_0},} \\ {{x_t}\left( \theta \right) = x\left( {t + \theta } \right),{\kern 1pt} - h \leqslant \theta \leqslant 0,{\kern 1pt} x:{J_x} \to {R^n}.} \end{array}} \right\}$$ Here ξ : [t₀, ∞) → Rl is the standard Wiener process, and the continuous functionals a_l, a₂ are defined on [t₀, ∞) × C[−h, 0]. The initial condition for (1.1) is 1.2$${x_{{t_o}}} = \phi $$