Reconstruction of stochastic dynamical equations: exemplary diffusion, jump-diffusion processes and lévy noise-driven langevin dynamics

Rahimi Tabar, M. R ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-030-18472-8_21
  3. Publisher: Springer Verlag , 2019
  4. Abstract:
  5. In this chapter we reconstruct stochastic dynamical equations with known drift and diffusion coefficients, as well as known properties of jumps, jump amplitude and jump rate from synthetic time series, sampled with time interval τ. The examples have Langevin (white noise- and Lévy noise-driven) and jump-diffusion dynamical equations. We also study the estimation of the Kramers–Moyal coefficients for “phase” dynamics that enable us to investigate the phenomenon of synchronisation in systems with interaction. © 2019, Springer Nature Switzerland AG
  6. Keywords:
  7. Lévy driven Langevin dynamics ; Phase dynamics ; Reconstruction ; Stationary processes ; Stochastic dynamics ; Synchronisation ; Synthetic time series
  8. Source: Understanding Complex Systems ; 2019 , Pages 227-241 ; 18600832 (ISSN)
  9. URL: https://link.springer.com/chapter/10.1007/978-3-030-18472-8_21