Abstract
A scalar Langevin-type process that is driven by Ornstein-Uhlenbeck noise is non-Markovian. However, the joint dynamics of and is described by a Markov process in two dimensions. But even though there exists a variety of techniques for the analysis of Markov processes, it is still a challenge to estimate the process parameters solely based on a given time series of . Such a partially observed 2D process could, e.g., be analyzed in a Bayesian framework using Markov chain Monte Carlo methods. Alternatively, an embedding strategy can be applied, where first the joint dynamics of and its temporal derivative is analyzed. Subsequently, the results can be used to determine the process parameters of and . In this paper, we propose a more direct approach that is purely based on the moments of the increments of , which can be estimated for different time-increments from a given time series. From a stochastic Taylor expansion of , analytic expressions for these moments can be derived, which can be used to estimate the process parameters by a regression strategy.
- Received 4 February 2017
- Revised 14 December 2017
DOI:https://doi.org/10.1103/PhysRevE.97.012113
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