LEADER 06621nam 22008175 450 001 9910337876203321 005 20220622111350.0 010 $a3-030-18472-2 024 7 $a10.1007/978-3-030-18472-8 035 $a(CKB)4100000008618162 035 $a(DE-He213)978-3-030-18472-8 035 $a(MiAaPQ)EBC5926189 035 $a(PPN)238489132 035 $a(EXLCZ)994100000008618162 100 $a20190704d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems$b[electronic resource] $eUsing the Methods of Stochastic Processes /$fby M. Reza Rahimi Tabar 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVIII, 280 p. 41 illus., 22 illus. in color.) 225 1 $aUnderstanding Complex Systems,$x1860-0832 311 $a3-030-18471-4 327 $a1 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. 330 $aThis book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements. 410 0$aUnderstanding Complex Systems,$x1860-0832 606 $aProcessos estocàstics$2thub 606 $aSistemes complexos$2thub 606 $aAnàlisi de sèries temporals$2thub 606 $aStatistical physics 606 $aDynamical systems 606 $aSystem theory 606 $aProbabilities 606 $aEconomic theory 606 $aComputational complexity 606 $aNeurosciences 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M13090 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 606 $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022 606 $aNeurosciences$3https://scigraph.springernature.com/ontologies/product-market-codes/B18006 608 $aLlibres electrònics$2thub 615 7$aProcessos estocàstics 615 7$aSistemes complexos 615 7$aAnàlisi de sèries temporals 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aSystem theory. 615 0$aProbabilities. 615 0$aEconomic theory. 615 0$aComputational complexity. 615 0$aNeurosciences. 615 14$aComplex Systems. 615 24$aComplex Systems. 615 24$aProbability Theory and Stochastic Processes. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 615 24$aComplexity. 615 24$aNeurosciences. 676 $a519.2 700 $aRahimi Tabar$b M. Reza$4aut$4http://id.loc.gov/vocabulary/relators/aut$01058784 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910337876203321 996 $aAnalysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems$92502494 997 $aUNINA