The nonparametric LAN expansion for discretely observed diffusions

@article{Wang2018TheNL,
  title={The nonparametric LAN expansion for discretely observed diffusions},
  author={Sven Wang},
  journal={arXiv: Statistics Theory},
  year={2018}
}
  • Sven Wang
  • Published 2018
  • Mathematics
  • arXiv: Statistics Theory
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… Expand

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