Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point

In this chapter we shall consider perturbations of a dynamical system $$ {\dot x_t} = b({x_t}),\quad {{\text{x}}_{\text{0}}}{\text{ = x,}}\quad b(x) = ({b^1}(x),...,{b^r}(x))$$ (1.1) by a white noise process or by a Gaussian process in general.