Parameter-free resolution of the superposition of stochastic signals

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• 作者：Teresa Scholz^a ; ^{tascholz@fc.ul.pt} ; Frank Raischel^b ; ^c ; Vitor V. Lopes^d ; ^e ; Bernd Lehle^f ; Matthias Wä ; chter^f ; Joachim Peinke^f ; Pedro G. Lind^f ; ^g
• 关键词：Stochastic processes ; Measurement noise ; Observational noise ; Signal reconstruction ; Signals superposition
• 刊名：Physics Letters A
• 出版年：2017
• 出版时间：30 January 2017
• 年：2017
• 卷：381
• 期：4
• 页码：194-206
• 全文大小：1023 K
• 卷排序：381

文摘

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent stochastic processes, one of which is an Ornstein–Uhlenbeck process and the other a general (non-linear) Langevin process. The method is able to distinguish between the stochastic processes, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.