标题： 小扩散基于离散观测的拟合优度检验 显示英文标题

标题： Goodness of fit test for small diffusions by discrete observations

摘要： 我们研究了一维小扩散漂移系数的非参数拟合优度检验问题。 我们的检验基于过程的离散观测，并且扩散系数是一个需要在检验过程中估计的 nuisance 函数。 我们证明了检验的极限分布是标准布朗运动的上确界，因此我们的检验渐近无分布依赖性。 我们还证明了我们的检验在任何固定的替代假设下具有一致性。 显示英文摘要

摘要： We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent under any fixed alternatives.