A criterion for convergence of continuous stochastic approximation procedures

For the a.s. convergence of the stochastic approximation procedure
$$ dX_s=\alpha(s)[\triangledown f(X_s)+\varphi(s,X_s)]\,ds+\beta(s)\sigma(s,X_s)\,dW_s $$
to a maximum point of $f$, the following condition is proved to be necessary and sufficient: for any $\lambda>0$
$$ \int_0^{\infty}\exp(-\lambda\gamma^{-2}(t))\,dt<\infty $$
where $dt=\alpha(s)\,ds$; $\gamma(t)=\beta(t)/\sqrt{\alpha(t)}$.