Nonparametric estimation of linear multiplier for processes driven by a bifractional Brownian motion

We study the problem of nonparametric estimation of the linear multiplier function θ(t) for processes satisfying stochastic differential equations of the type dXₜ=θ(t)Xₜdt+ε dWₜH,K, X₀=x₀,0≤ t ≤ T where ₜH,K, t ≥ 0\ is a bifractional Brownian motion with known parameters H∈ (0,1), K∈ (0,1] and HK∈ (1/2,1). We investigate the asymptotic behaviour of the estimator of the unknown function θ(t) as ε → 0.