E-Book, Englisch, 280 Seiten, eBook
Rahimi Tabar Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems
Erscheinungsjahr 2019
ISBN: 978-3-030-18472-8
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark
Using the Methods of Stochastic Processes
E-Book, Englisch, 280 Seiten, eBook
Reihe: Understanding Complex Systems
ISBN: 978-3-030-18472-8
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark
Zielgruppe
Graduate
Autoren/Hrsg.
Weitere Infos & Material
1 Introduction.- 2 Introduction to Stochastic Processes.- 3 Kramers-Moyal Expansion and Fokker-Planck Equation.- 4 Continuous Stochastic Process.- 5 The Langevin Equation and Wiener Process.- 6 Stochastic Integration, It^o and Stratonovich Calculi.- 7 Equivalence of Langevin and Fokker-Planck Equations.- 8 Examples of Stochastic Calculus.- 9 Langevin Dynamics in Higher Dimensions.- 10 Levy Noise Driven Langevin Equation and its Time Series-Based Reconstruction.- 11 Stochastic Processes with Jumps and Non-Vanishing Higher-Order Kramers-Moyal Coefficients.- 12 Jump-Diffusion Processes.- 13 Two-Dimensional (Bivariate) Jump-Diffusion Processes.- 14 Numerical Solution of Stochastic Differential Equations: Diffusion and Jump-Diffusion Processes.- 15 The Friedrich-Peinke Approach to Reconstruction of Dynamical Equation for Time Series: Complexity in View of Stochastic Processes.- 16 How To Set Up Stochastic Equations For Real-World Processes: Markov-Einstein Time Scale.- 17 Reconstruction of Stochastic Dynamical Equations: Exemplary Stationary Diffusion and Jump-Diffusion Processes.- 18 The Kramers-Moyal Coefficients of Non-Stationary Time series in The Presence of Microstructure (Measurement) Noise.- 19 Influence of Finite Time Step in Estimating of the Kramers-Moyal Coefficients.- 20 Distinguishing Diffusive and Jumpy Behaviors in Real-World Time Series.- 21 Reconstruction of Langevin and Jump-Diffusion Dynamics From Empirical Uni- and Bivariate Time Series.- 22 Applications and Outlook.- 23 Epileptic Brain Dynamics.