Asymptotic normality of least squares estimators to stochastic differential equations driven by fractional Brownian motions

12/23/2021

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by   Yasutaka Shimizu, et al.

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We will consider the following stochastic differential equation (SDE): X_t=X_0+∫_0^tb(X_s,θ_0)ds+σ B_t,   t∈(0,T], where {B_t}_t≥ 0 is a fractional Brownian motion with Hurst index H∈(1/2,1), θ_0 is a parameter that contains a bounded and open convex subset Θ⊂ℝ^d, {b(·,θ),θ∈Θ} is a family of drift coefficients with b(·,θ):ℝ→ℝ, and σ∈ℝ is assumed to be the known diffusion coefficient.