有限时间漂移和扩散系数的精确修正
Exact corrections for finite-time drift and diffusion coefficients
摘要：
实际数据被限制到有限的采样率，这要求对动态方程的有限时间估计的校正进行适当的数学描述。通常在文献中，考虑低阶离散时间近似的建模扩散过程。另一方面，缺乏基于高阶近似的简单估计程序。对于标准的扩散模型，其中包括加性和乘性噪声分量，我们得到的经验有限时间漂移和扩散系数的精确校正，基于Itô-Taylor展开。这些结果允许从经验估计重建真正的隐藏系数。我们还推导出第三和第四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查。一些代表性的人工时间序列的数值结果的理论预测进行了比较。
英文摘要：
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on Itô-Taylor expansions. 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 that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series.
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