Estimation of the diffusion coefficient under strong mixing

We consider an estimate of the diffusion coefficient which arises in a stochastic differential equation, defining a certain time-continuous process. The used equation is: d(X)t = sigma(X-t)dW(t), t is an element of R+ where (W-t; t is an element of R+) is a standard Brownian motion and sigma is the diffusion coefficient. We obtain the pointwise and uniform almost sure consistency for the kernel estimate of the diffusion coefficient under a strong mixing condition.