On low-sampling-rate Kramers-Moyal coefficients

TL;DR

This paper investigates how sampling intervals affect the estimation of Kramers-Moyal coefficients, providing finite-time formulas for standard processes and analyzing extreme cases to improve data-driven analysis accuracy.

Contribution

It introduces finite-time expressions for Kramers-Moyal coefficients across various processes and examines extreme sampling scenarios to guide better data analysis.

Findings

Finite-time formulas for standard processes.

Analysis of independence and no-fluctuation limits.

Guidelines for accurate coefficient estimation.

Abstract

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.