Nonparametric identification for difiusion processes

Abstract

Recalling that the first order density function of a stationary diffusion process satifies a differential equation which can be derived from the forward equation of Kolmogorov and using nonparametric density estimation, an alternative approach to the estimation of the drift function is presented. Sufficient conditions on a measurable stationary process are given which ensure weak consistency estimation of the logarithmic derivative of its first order density function. Assumptions on a differential stochastic equation driven by Brownian motion are presented under which its stationary solution satisfies the above sufficient identifiability conditions.