On minimum-contrast estimation for hilbert space-valued stochastic differential equations

Abstract

In this note a family of minimum contrast functions is introduced for estimating a real parameter appearing in a linear, stationary stochastic differential equation assuming values in a real and separable Hilbert space. It is proved that the corresponding minimum contrast estimate based on a noise free, direct, time continuous measurement of sample path is asymptotically consistent and has an asymptotic normal distribution.

Keywords:

• Minimum contrast estimation
• stochastic evolutions
• mild solutions