论文标题
固定时间序列的随机微分方程的非参数估计
Non-parametric estimation of Stochastic Differential Equations from stationary time-series
论文作者
论文摘要
我们研究了长期固定轨迹的非参数估计（由布朗运动驱动的随机微分方程）的效率。首先，我们基于条件期望引入估计量，这是由于漂移和扩散系数的定义所激发的。这些估计器涉及从离散绘制的固定数据计算预期值的时间和空间散布参数。接下来，我们根据计算参数分析这些估计器的一致性和平方误差。我们得出观测点的数量，时间和空间散布参数之间的关系，以实现收敛的最佳速度并最大程度地减少计算复杂性。我们通过数值模拟说明了我们的方法。
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is motivated by the definition of drift and diffusion coefficients. These estimators involve time- and space-discretization parameters for computing expected values from discretely-sampled stationary data. Next, we analyze consistency and mean squared error of these estimators depending on computational parameters. We derive relationships between the number of observational points, time- and space-discretization parameters in order to achieve the optimal speed of convergence and minimize computational complexity. We illustrate our approach with numerical simulations.
