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基于独立同分布随机微分方程路径的非参数漂移估计AI 解读

We consider $N$ independent stochastic processes $(X_{i}(t),t\in [0,T])$, $i=1,\ldots ,N$, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval $[0,T]$ where $T$ is fixed. We study nonparametric estimation of the drift function on a given subset $A$ of ${\mathbb{R}}$. Projection estimators are defined on finite dimensional subsets of ${\mathbb{L}}^{2}(A,dx)$. We stress that the set $A$ may be compact or not…

非参数扩散与欧拉离散格式统计实验的渐近等价性AI 解读

We prove a global asymptotic equivalence of experiments in the sense of Le Cam’s theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme…

长时间区间内基于高频数据的 Lévy 过程估计AI 解读

In this paper, we study nonparametric estimation of the Lévy density for Lévy processes, with and without Brownian component. For this, we consider n discrete time observations with step Δ. The asymptotic framework is: n tends to infinity, Δ=Δn tends to zero while nΔn tends to infinity. We use a Fourier approach to construct an adaptive nonparametric estimator of the Lévy density and to provide a bound for the global ${\mathbb{L}}^{2}$-risk. Estimators of the drift and of…

Poisson 强度估计与正漂移扩散估计的渐近等价性AI 解读

We consider a diffusion model of small variance type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model in the sense of asymptotic equivalence of experiments. It is shown that observation of the diffusion process until its first hitting time of level one is a natural model for the purpose of inference on the drift density. The diffusion model can be discretized by the collection of level crossing times…