Qualitative and quantitative analysis of stochastic processes based on measured data, I: Theory and applications to synthetic data

摘要

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-para metric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to decomposition of process dynamics into deterministic and random components. Such decomposition provides a basis for qualitative and quantitative analysis of process dynamics. In Part 1, the following analysis possibilities are described and illustrated using various synthetic datasets: (1) qualitative inspection of the estimated terms presented as fields, (2) reconstruction of the deterministic and stochastic evolution of the process and (3) approximation of the deterministic term by an analytical function and quantitative treatment of the equations obtained. In Part 11, these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding. (C) 2002 Elsevier Science Ltd. All rights reserved. [References: 20]