Potentials of Unbalanced Complex Kinetics Observed in Market Time Series
  As a model of market price, we introduce a new type of random walk in a moving potential which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks are similar to those of ordinary random walks for large time scales; however, their short time properties are approximated by abnormal diffusion with non-trivial exponents. A new data analysis method based on this model enables us to observe temporal changes of potential forces from high precision market data directly. 
Misako Takayasu, Takayuki Mizuno, Hideki Takayasu