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

• Κύριος συγγραφέας: Rahimi Tabar, M. Reza (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Understanding Complex Systems,
• Θέματα: Statistical physics.; Dynamical systems.; System theory.; Probabilities.; Economic theory.; Computational complexity.; Neurosciences.; Complex Systems.; Probability Theory and Stochastic Processes.; Economic Theory/Quantitative Economics/Mathematical Methods.; Complexity.

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristi...

Πίνακας περιεχομένων:

• 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.