title: Low-sampling-rate Kramers-Moyal coefficients.
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.
authors.affiliation: Department of Physics, PUC-Rio and National Institute of Science and Technology for Complex Systems, Rua Marquês de São Vicente 225, Gávea, CEP 22453-900 Rio de Janeiro, RJ, Brazil.
authors.forename: C
authors.initials: C
authors.lastname: Anteneodo
authors.forename: S M
authors.initials: SM
authors.lastname: Duarte Queirós