ESTIMATION OF A PARAMETER OF A KNOWN LAW OF A PROBABILITY BY STOCHASTIC APPROXIMATIONS

We consider a stochastic approximation process in a non-empty closed convex set K of R: Xn+1 = Π(Xn −An(X1,X2, ...,Xn)Ψn(Yn;Xn)), with for each n, E[Ψn(Yn; θn)] = 0, and Π is the projection operator on K. We denote Tn the sub-σ-algebra generated by the events before time n. We prove two theorems of almost sure convergence for the process (Xn) and we give two applications for estimation of a parameter of a known law of probability. AMS Subject Classification: 62L20