Financial Brownian particle in the layered order book fluid and   Fluctuation-Dissipation relations
  We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner-layer, the correlation is strong and with short memory while, in the outer-layer, it is weaker and with long memory. By interpreting and estimating the contribution from the outer-layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation (FDR) in this non-material Brownian motion process. 
Yoshihiro Yura and Hideki Takayasu and Didier Sornette and Misako   Takayasu
q-fin.TR physics.data-an physics.soc-ph