title: Financial Brownian particle in the layered order-book fluid and fluctuation-dissipation relations.
abstract: 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 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 in this nonmaterial Brownian motion process.
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology 4259 Nagatsuta-cho, Yokohama 226-8502, Japan and Department of Management, Technology, and Economics, ETH Zurich, Scheuchzerstrasse 7, 8092 Zurich, Switzerland.
authors.forename: Yoshihiro
authors.initials: Y
authors.lastname: Yura
authors.affiliation: Sony Computer Science Laboratories, 3-14-13, Higashi-Gotanda, Shinagawa-ku, Tokyo 141-0022, Japan and Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan.
authors.forename: Hideki
authors.initials: H
authors.lastname: Takayasu
authors.affiliation: Department of Management, Technology, and Economics, ETH Zurich, Scheuchzerstrasse 7, 8092 Zurich, Switzerland.
authors.forename: Didier
authors.initials: D
authors.lastname: Sornette
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology 4259 Nagatsuta-cho, Yokohama 226-8502, Japan.
authors.forename: Misako
authors.initials: M
authors.lastname: Takayasu