## Electronic Journal of Statistics

### The nonparametric LAN expansion for discretely observed diffusions

Sven Wang

#### Abstract

Consider a scalar reflected diffusion $(X_{t}:t\geq 0)$, where the unknown drift function $b$ is modelled nonparametrically. We show that in the low frequency sampling case, when the sample consists of $(X_{0},X_{\Delta },...,X_{n\Delta })$ for some fixed sampling distance $\Delta >0$, the model satisfies the local asymptotic normality (LAN) property, assuming that $b$ satisfies some mild regularity assumptions. This is established by using the connections of diffusion processes to elliptic and parabolic PDEs. The key tools used are regularity estimates for certain parabolic PDEs as well as a detailed analysis of the spectral properties of the elliptic differential operator related to $(X_{t}:t\geq 0)$.

#### Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 1329-1358.

Dates
First available in Project Euclid: 5 April 2019

https://projecteuclid.org/euclid.ejs/1554451244

Digital Object Identifier
doi:10.1214/19-EJS1545

Mathematical Reviews number (MathSciNet)
MR3935851

Zentralblatt MATH identifier
07056153

Subjects
Primary: 62M99: None of the above, but in this section

#### Citation

Wang, Sven. The nonparametric LAN expansion for discretely observed diffusions. Electron. J. Statist. 13 (2019), no. 1, 1329--1358. doi:10.1214/19-EJS1545. https://projecteuclid.org/euclid.ejs/1554451244

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