Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems: Using the Methods of Stochastic Processes

Front Matter ....Pages i-xviii
 Introduction  (M. Reza Rahimi Tabar)....Pages 1-8
 Introduction to Stochastic Processes  (M. Reza Rahimi Tabar)....Pages 9-18
 Kramers–Moyal Expansion and Fokker–Planck Equation  (M. Reza Rahimi Tabar)....Pages 19-29
 Continuous Stochastic Processes  (M. Reza Rahimi Tabar)....Pages 31-37
 The Langevin Equation and Wiener Process  (M. Reza Rahimi Tabar)....Pages 39-48
 Stochastic Integration, Itô and Stratonovich Calculi  (M. Reza Rahimi Tabar)....Pages 49-60
 Equivalence of Langevin and Fokker–Planck Equations  (M. Reza Rahimi Tabar)....Pages 61-68
 Example of Stochastic Calculus  (M. Reza Rahimi Tabar)....Pages 69-78
 Langevin Dynamics in Higher Dimensions  (M. Reza Rahimi Tabar)....Pages 79-86
 Lévy Noise-Driven Langevin Equation and Its Time Series–Based Reconstruction   (M. Reza Rahimi Tabar)....Pages 87-98
 Stochastic Processes with Jumps and Non-vanishing Higher-Order Kramers–Moyal Coefficients  (M. Reza Rahimi Tabar)....Pages 99-110
 Jump-Diffusion Processes  (M. Reza Rahimi Tabar)....Pages 111-121
 Two-Dimensional (Bivariate) Jump-Diffusion Processes  (M. Reza Rahimi Tabar)....Pages 123-128
 Numerical Solution of Stochastic Differential Equations: Diffusion and Jump-Diffusion Processes  (M. Reza Rahimi Tabar)....Pages 129-142
 The Friedrich–Peinke Approach to Reconstruction of Dynamical Equation for Time Series: Complexity in View of Stochastic Processes  (M. Reza Rahimi Tabar)....Pages 143-164
 How to Set Up Stochastic Equations for Real World Processes: Markov–Einstein Time Scale  (M. Reza Rahimi Tabar)....Pages 165-179
 The Kramers–Moyal Coefficients of Non-stationary Time Series and in the Presence of Microstructure (Measurement) Noise  (M. Reza Rahimi Tabar)....Pages 181-189
 Influence of Finite Time Step in Estimating of the Kramers–Moyal Coefficients  (M. Reza Rahimi Tabar)....Pages 191-205
 Distinguishing Diffusive and Jumpy Behaviors in Real-World Time Series  (M. Reza Rahimi Tabar)....Pages 207-213
 Reconstruction Procedure for Writing Down the Langevin and Jump-Diffusion Dynamics from Empirical Uni- and Bivariate Time Series  (M. Reza Rahimi Tabar)....Pages 215-226
 Reconstruction of Stochastic Dynamical Equations: Exemplary Diffusion, Jump-Diffusion Processes and Lévy Noise-Driven Langevin Dynamics  (M. Reza Rahimi Tabar)....Pages 227-241
 Applications and Outlook  (M. Reza Rahimi Tabar)....Pages 243-260
 Epileptic Brain Dynamics  (M. Reza Rahimi Tabar)....Pages 261-271
 Correction to: Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems  (M. R. Rahimi Tabar)....Pages C1-C1
Back Matter ....Pages 273-280