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].
CITATION STYLE
Tabar, M. R. R. (2019). Influence of Finite Time Step in Estimating of the Kramers–Moyal Coefficients. In Understanding Complex Systems (pp. 191–205). Springer Verlag. https://doi.org/10.1007/978-3-030-18472-8_18
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