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The maximum likelihood type estimator of SDEs with fractional Brownian motion under small noise asymptotics in the rough case
Shohei Nakajima
https://arxiv.org/abs/2406.07804

The maximum likelihood type estimator of SDEs with fractional Brownian motion under small noise asymptotics in the rough case
We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood estimator and establish its the asymptotic normality and moment convergence of the drift parameter when a small dispersion coefficient vanishes.

This https://arxiv.org/abs/2306.16272 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Estimation of several parameters in discretely-observed Stochastic Differential Equations with additive fractional noise
We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of the Hurst parameter, the diffusion parameter and the drift, which lies in a parametrised family of coercive drift coefficients. Our procedure is based on the assumption that the stationary distribution of the SDE and of its increments permits to iden…