论文标题
粘性扩散的当地时间的功能收敛
Functional convergence to the local time of a sticky diffusion
论文作者
论文摘要
我们基于高频观测值建立了在粘性阈值下扩散的局部时间近似的一致性。首先，我们证明了粘稠的布朗运动的结果，然后将其扩散到ITô扩散，并用粘点（SID）延伸。为此，我们得出SID的路径公式以及相应的关键随机演算结果（ItôFormula，Girsanov Theorem）。根据当地时间近似，我们为粘性参数开发了一致的估计器。我们以数值实验结束，并评估粘性估计器的统计特性和局部时间近似。
We establish the consistency of a local time approximation of a diffusion at a sticky threshold based on high-frequency observations. First, we prove the result for sticky Brownian motion, and then extend it to Itô diffusions with a sticky point (SID). For this, we derive the pathwise formulation of an SID along with respective versions of key stochastic calculus results (Itô formula, Girsanov theorem). Based on the local time approximation, we develop a consistent estimator for the stickiness parameter. We conclude with numerical experiments and assess statistical properties of the stickiness estimator and the local time approximation.
