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Influence of finite time step in estimating of the kramers–moyal coefficients

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_18
  3. Publisher: Springer Verlag , 2019
  4. Abstract:
  5. Data sampled at discrete times appear as successions of discontinuous jump events, even if the underlying trajectory is continuous. In this chapter we study finite sampling τ expansion of the Kramers-Moyal conditional moments for the Langevin and jump-diffusion dynamics. Using the expansion for the Langevin dynamics, we introduce a criterion to validate the method numerically, namely, the Pawula theorem, to judge whether the fourth-order KM moment tends to zero. The criterion is a relation between the fourth- and second-order KM conditional moments for small time lag τ [1]. © 2019, Springer Nature Switzerland AG
  6. Keywords:
  7. Expansion of kramers–moyal conditional moments ; Finite sampling ; Numerical verification of pawula theorem
  8. Source: Understanding Complex Systems ; 2019 , Pages 191-205 ; 18600832 (ISSN)
  9. URL: http://link-springer-com-443.webvpn.fjmu.edu.cn/chapter/10.1007%2F978-3-030-18472-8_18