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.

We generalize the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting, and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number of particles in the inner layer and its change per unit time, where the inner layer is revealed by the correlations between price velocity and change in the number of particles (limit orders). This allows us to introduce the Knudsen number of the financial Brownian particle motion and its asymmetric version (on the buy and sell sides). Not being considered previously, the asymmetric Knudsen numbers are crucial in finance in order to detect asymmetric price changes. The Knudsen numbers allows us to characterize the conditions for the market dynamics to be correctly described by a continuous stochastic process. Not questioned until now for large liquid markets such as the USD-JPY and EUR-USD exchange rates, we show that there are regimes when the Knudsen numbers are so high that discrete particle effects dominate, such as during market stresses and crashes. We document the presence of imbalances of particles depletion rates on the buy and sell sides that are associated with high Knudsen numbers and violent directional price changes. This indicator can detect the direction of the price motion at the early stage while the usual volatility risk measure is blind to the price direction.

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)

We apply the particle filter for the quick and accurate estimation of a switching point in a financial market based on a recently developed theoretical model, the potentials of unbalanced complex kinetics (PUCK) model, which fulfils all empirically stylized facts such as fat-tailed distribution of price changes and the anomalous diffusion in a short-time scale. We show the efficiency of an optimized driving force in particle filtering for the estimation of the parameters of the PUCK model, using a simulation study. As an example, we apply the method to the dollar-yen exchange market before and after the biggest earthquake in Japan in March 2011. With this fast and efficient estimation method, we can clearly confirm that the statistics of the time series of exchange rate changed drastically at the time of the arrival of the quake in Tokyo area, implying that the earthquake worked as a trigger for the market's switching point.