Rate of decay for solutions of stochastic differential equations

A theorem is given which demonstrates that solutions of a stochastic differential equation decay to zero at least as fast as a function ψ(t) provided $\text{L}\text{ln}\text{V] ?}\text{(d}\text{dt)}\text{(}\text{ln}\text{ψ)}$, where V is a Liapunov-like function and L is the operator associated with the stochastic equation. The result is an extension of a recent result of A. Friedman and M. Pinsky. A further generalization is discussed.