The stochastic harmonic oscillator with finite correlation times

The moments of an undamped stochastic harmonic oscillator are examined using iteration procedures described in earlier papers. The noise is similar to white noise, but has finite correlation time which is taken to be less than the period of the oscillator. When the time of observation is finite, the first moment is explicitly given, attempting first-order approximation. For infinite time, we establish certain conditions which assure boundedness of the first and second moments. All the results obtained are applied to the white noise when its correlation time is considered finite.