Title: Non-parametric estimation of a Langevin model driven by correlated noise Show Chinese title

Title: 由相关噪声驱动的Langevin模型的非参数估计

Abstract: Langevin models are frequently used to model various stochastic processes in different fields of natural and social sciences. They are adapted to measured data by estimation techniques such as maximum likelihood estimation, Markov chain Monte Carlo methods, or the non-parametric direct estimation method introduced by Friedrich et al. The latter has the distinction of being very effective in the context of large data sets. Due to their $\delta$-correlated noise, standard Langevin models are limited to Markovian dynamics. A non-Markovian Langevin model can be formulated by introducing a hidden component that realizes correlated noise. For the estimation of such a partially observed diffusion a different version of the direct estimation method was introduced by Lehle et al. However, this procedure includes the limitation that the correlation length of the noise component is small compared to that of the measured component. In this work we propose another version of the direct estimation method that does not include this restriction. Via this method it is possible to deal with large data sets of a wider range of examples in an effective way. We discuss the abilities of the proposed procedure using several synthetic examples. Show Chinese abstract

Abstract: Langevin模型常用于不同自然科学和社会科学领域的各种随机过程建模。 它们通过最大似然估计、马尔可夫链蒙特卡洛方法或Friedrich等人引入的非参数直接估计方法等估计技术来适应测量数据。 后者在大规模数据集的背景下表现出极高的有效性。 由于其$\delta$相关的噪声，标准Langevin模型仅限于马尔可夫动力学。 通过引入一个实现相关噪声的隐藏组件，可以构建非马尔可夫Langevin模型。 对于此类部分观测扩散的估计，Lehle等人引入了直接估计方法的一种不同版本。 然而，此过程存在一个限制，即噪声成分的相关长度相比测量成分的相关长度较小。 在本工作中，我们提出了一种不包含此限制的直接估计方法的另一种版本。 通过这种方法，可以有效地处理更广泛范围内的大型数据集。 我们使用多个合成示例讨论了所提出方法的能力。