umpdiff: A Python Library for Statistical Inference of Jump-Diffusion Processes in Observational or Experimental Data Sets

umpdiff: A Python Library for Statistical Inference of Jump-Diffusion Processes in Observational or Experimental Data Sets

stochastic differential equations, jump-diffusion processes, Kramers-Moyal expansion, Kramers-Moyal coefficients, Python.

We introduce a Python library, called jumpdiff, which includes all necessary functions to assess jump-diffusion processes. This library includes functions which compute
a set of non-parametric estimators of all contributions composing a jump-diffusion process, namely the drift, the diffusion, and the stochastic jump strengths. Having a set of
measurements from a jump-diffusion process, jumpdiff is able to retrieve the evolution
equation producing data series statistically equivalent to the series of measurements. The
back-end calculations are based on second-order corrections of the conditional moments
expressed from the series of Kramers-Moyal coefficients. Additionally, the library is also
able to test if stochastic jump contributions are present in the dynamics underlying a set
of measurements. Finally, we introduce a simple iterative method for deriving secondorder corrections of any Kramers-Moyal coefficient.

Leonardo Rydin Gorjão
NMBU

https://www.jstatsoft.org/article/view/v105i04

Forschungszentrum Jülich,
University of Cologne

January 2023

Fajar Bagus W

PDF

English

Text