在奥氏条件下非紧支撑上遍历扩散过程扩散系数的非参数估计
Nonparametric estimation of the diffusion coefficient of an ergodic diffusion process on non-compact supports under Osgood's conditions
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中文总结 AI 辅助
研究非紧支撑上遍历扩散过程平方扩散系数的非参数估计，核心方法是投影到有限维空间构造估计量，贡献为建立风险界、收敛速率，进行模型选择并通过模拟数据完善理论结果。
中文摘要 AI 辅助
本文研究非紧支撑上遍历扩散过程平方扩散系数的非参数估计，此时随机微分方程的两个系数属于比赫尔德连续函数空间更大的空间。通过投影到有限维空间构造估计量，避免维度截断。建立了非自适应估计量的风险界以及有界和无界扩散系数的显式收敛速率。进行了模型选择过程，并利用塔拉格兰德不等式推导风险界。最后通过对模拟数据的数值研究完善了理论结果。
英文摘要
In this paper, we study the nonparametric estimation of the squared diffusion coefficient of an ergodic diffusion process on non-compact supports, when the two coefficients of the stochastic differential equation belong to a space larger than the space of Hölder continuous functions. The estimators are constructed by projection onto finite-dimensional spaces, thereby avoiding truncation of the dimension. We establish risk bounds of non-adaptive estimators and explicit rates of convergence for bounded and unbounded diffusion coefficients. A model selection procedure is performed, followed by the derivation of risk bounds using Talagrand's inequality. The theoretical results are completed with a numerical study over simulated data.
