Friedrich R, Peinke J, Renner C
Institute fur Theoretische Physik, Universitat Stuttgart, D-70550 Stuttgart, Germany.
Phys Rev Lett. 2000 May 29;84(22):5224-7. doi: 10.1103/PhysRevLett.84.5224.
It is shown that price changes of the U.S. dollar-German mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore, we show how Kramers-Moyal coefficients can be estimated from the empirical data. Finally, we present an explicit Fokker-Planck equation which models very precisely the empirical probability distributions, in particular, their non-Gaussian heavy tails.
结果表明，美元兑德国马克汇率在不同延迟时间的价格变化可被视为一个随机马尔可夫过程。此外，我们展示了如何从经验数据中估计克莱默斯-莫亚尔系数。最后，我们给出了一个明确的福克-普朗克方程，该方程能非常精确地模拟经验概率分布，特别是它们的非高斯重尾分布。
