Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 28: Nonlinear stochastic systems

DY 28.8: Talk

Thursday, March 29, 2007, 15:45–16:00, H2

Analysis of Nonstationary Stochastic Processes with Application to the Fluctuations in the Oil Price — •Fatemeh Ghasemi¹, Mohammad Reza Rahimi Tabar^2,3, Muhammad Sahimi⁴, Joachim Peinke⁵, and Rudolf Friedrich⁶ — ¹The Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany — ²Dep. of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran 11365, Iran — ³CNRS UMR 6529, Observatoire de la Côte d’Azur, BP 4229, 06304 Nice Cedex 4, France — ⁴Mork Family Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles,CA 90089-1211 — ⁵Carl von Ossietzky University, Institute of Physics, D-26111 Oldenburg, Germany — ⁶Institute for Theoretical Physics, University of Münster, D-48149 Münster, Germany

We describe a method for analyzing a nonstationary stochastic process, and utilize it to study the fluctuations in the oil price. Evidence is presented that the fluctuations in the returns constitute a Markov process, characterized by a Markov time scale t_M. We compute the coefficients of the Kramers-Moyal expansion for the probability distribution function, and show that P(y,t|,y₀,t₀) satisfies a Fokker-Planck equation, which is equivalent to a Langevin equation for y(t). The Langevin equation provides quantitative predictions for the oil price over Markov time scale t_M. The method described is applicable to a wide variety of nonstationary stochastic processes.