Sunday, April 6, 2008

[AD 5] New model: "PL VAC + Gaussian Noise + X"

Since we are not interested in shaped noise, the following concept would be more transparent:

The PL-VAC creates a trajectory with rich internal structure (a succession of more diffusive and more ballistic phases) and yields the correct MSD/VAC/PSD at medium and long times. It also makes the kurtosis slightly negative at long times.

Gaussian White Noise is added to the trajectory at the end. It only serves to produce a plateau in the MSD.

Another, yet unidentified Process X is reponsible for the positive kurtosis at small times.

Process X should have the following properties:
  • No significant distortion of the MSD/VAC/PSD
  • Produce increasingly non-Gaussian step width distributions with positive kurtosis as the lag time become small.
  • Candidate: Modulated Poisson Statistics.

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