Nonparametric methods of nonlinear filtering of stationary random sequences (Q794610)

A nonlinear method is proposed for filtering of strictly stationary ergodic random Markov sequence observed in noise. The state equation and the distribution of the signal is assumed to be unknown. The conditional probability density of observations is assumed to be of exponential type. The mean-square convergence of nonparametric estimates of a multivariate probability density and the convergence of the gradient in the uniform metric are proved.