Parameters

JumpDiff.parameters.jump_amplitude(moments: numpy.ndarray, tol: float = 1e-10, full: bool = False, verbose: bool = True) → numpy.ndarray

Retrieves the jump amplitude xi (\(\xi\)) via

\[\lambda(x,t) = \frac{M_4(x,t)}{3\sigma_{\xi}^4}.\]

Take notice that the different normalisation of the moments leads to a different results.

Parameters:
  • moments (np.ndarray) – Moments extracted with the function moments. Needs moments up to order 6.
  • tol (float (defaul 1e-10)) – Toleration for the division of the moments.
  • full (bool (defaul False)) – If True returns also the (biased) weighed standard deviation of the averaging process.
  • verbose (bool (defaul True)) – Prints the result.
Returns:

xi_est – Estimator of the jump amplitude xi (\(\xi\)).
Return type:

np.ndarray

References

Anvari, M., Tabar, M. R. R., Peinke, J., Lehnertz, K., ‘Disentangling the stochastic behavior of complex time series.’ Scientific Reports, 6, 35435, 2016. doi: 10.1038/srep35435.

Lehnertz, K., Zabawa, L., and Tabar, M. R. R., ‘Characterizing abrupt transitions in stochastic dynamics.’ New Journal of Physics, 20(11):113043, 2018. doi: 10.1088/1367-2630/aaf0d7.

JumpDiff.parameters.jump_rate(moments: numpy.ndarray, xi_est: numpy.ndarray = None, tol: float = 1e-10, full: bool = False, verbose: bool = True) → numpy.ndarray

Retrieves the jump rate lamb (\(\lambda\)) via

\[\sigma_{\xi}^2 = \frac{M_6(x,t)}{5M_4(x,t)}.\]

Take notice that the different normalisation of the moments leads to a different results.

Parameters:
  • moments (np.ndarray) – moments extracted with the function ‘moments’. Needs moments of order 6.
  • tol (float (defaul 1e-10)) – Toleration for the division of the moments.
  • full (bool (defaul False)) – If True returns also the (biased) weighed standard deviation of the averaging process.
  • verbose (bool (defaul True)) – Prints the result.
Returns:

xi_est – Estimator on the jump rate lamb (\(\lambda\))
Return type:

np.ndarray

References

Anvari, M., Tabar, M. R. R., Peinke, J., Lehnertz, K., ‘Disentangling the stochastic behavior of complex time series.’ Scientific Reports, 6, 35435, 2016. doi: 10.1038/srep35435.

Lehnertz, K., Zabawa, L., and Tabar, M. R. R., ‘Characterizing abrupt transitions in stochastic dynamics.’ New Journal of Physics, 20(11):113043, 2018. doi: 10.1088/1367-2630/aaf0d7.