Anteneodo C, Riera R
Department of Physics, PUC-Rio and National Institute of Science and Technology for Complex Systems, CP 38071, 22452-970 Rio de Janeiro, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031103. doi: 10.1103/PhysRevE.80.031103. Epub 2009 Sep 3.
We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.
我们研究了一类具有线性漂移和二次扩散系数的标准扩散过程。这些对动态方程的贡献可以直接从数据时间序列中得出。然而，实际数据受到有限采样率的限制，因此建立所需有限时间校正的合适数学描述至关重要。基于伊藤 - 泰勒展开，我们给出了有限时间漂移和扩散系数的精确校正。这些结果使得能够从经验估计中重建真实的隐藏系数。我们还推导了三阶和四阶条件矩的高阶有限时间表达式，为这类扩散模型提供了额外的理论检验。将分析预测与代表性人工时间序列的数值结果进行了比较。
