Nonparametric Estimation of Linear Multiplier for Fractional Diffusion Processes

Abstract

We study the problem of nonparametric estimation of linear multiplier function θ(t) for processes satisfying stochastic differential equations of the type

where is a standard fractional Brownian motion with known Hurst index H ∈ (1/2, 3/4) and study the asymptotic behaviour of the estimator as ε → 0.

Keywords:

• Fractional Brownian motion
• Fractional diffusion process
• Linear multiplier
• Nonparametric estimation of trend

Mathematics Subject Classification:

• Primary 62M09
• Secondary 62G05