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

2024/06/12 by Б. Л. С. Пракаса Рао, Rao, B. L. S. Prakasa
Engineering · #60G22 #Advanced Control Systems Optimization #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2406.07889

openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of nonparametric estimation of the linear multiplier function θ(t) for processes satisfying stochastic differential equations of the type dX_t=θ(t)X_tdt+εdW_t^H,K, X₀=x₀,0≤ t ≤ T where \W_t^H,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.

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