Markov properties of high frequency exchange rate data

We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x,tau). This equation is completely determined by two coefficients D_{1}(x,tau) and D_{2}(x,tau) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck equation describe the empirical pdfs correctly, including the pronounced tails.Comment: 29 pages, 19 eps figures, misprints corrected, under consideration for publication in Physica

On the universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.Comment: 4 pages, 4 figure

Non-linear electrical response in a charge/orbital ordered Pr⁡0.63\Pr_{0.63}Ca0.37_{0.37}MnO3_3 crystal : the charge density wave analogy

Non-linear conduction in a charge-ordered manganese oxide Pr$_{0.63}$Ca$_{0.37}$MnO$_3$ is reported. To interpret such a feature, it is usually proposed that a breakdown of the charge or orbitally ordered state is induced by the current. The system behaves in such a way that the bias current may generate metallic paths giving rise to resistivity drop. One can describe this feature by considering the coexistence of localized and delocalized electron states with independent paths of conduction. This situation is reminiscent of what occurs in charge density wave systems where a similar non-linear conduction is also observed. In the light of recent experimental results suggesting the development of charge density waves in charge and orbitally ordered manganese oxides, a phenomenological model for charge density waves motion is used to describe the non-linear conduction in Pr$_{0.63}$Ca$_{0.37}$MnO$_3$. In such a framework, the non-linear conduction arises from the motion of the charge density waves condensate which carries a net electrical current.Comment: 13 pages, 6 figure