Local convergence theorems for adaptive stochastic approximation schemes - Lai, T. L. (1979)
For the regression model y = M(x) + ε, adaptive stochastic approximation schemes of the form x(n+1) = x(n) — y(n)/(nb(n)) for choosing the levels x(1),x(2),... at which y(1),y(2),... are observed converge with probability 1 to the unknown root θ of the regression function M(x). Certain local convergence theorems that relate the convergence rate of x(n) — θ to the limiting behavior of the random variables b(n) are established.