Nonparametric estimation of linear multiplier for processes driven by subfractional Brownian motion

Abstract

We study the problem of nonparametric estimation of linear multiplier function $\theta (t)$ for processes satisfying stochastic differential equations of the type $$d{X}_t=\theta (t)X_{t}dt+ϵd{\zeta }_t^H,X_0=x_0,0\le t\le T$$ where $\{{\zeta }_t^H,t\ge 0\}$ is a subfractional Brownian motion with known Hurst index H and study the asymptotic behavior of the estimator as $ϵ\to 0.$

Keywords:

• Nonparametric estimation
• linear multiplier
• subfractional Brownian motion

Mathematics Subject Classification:

• Primary 62M09
• Secondary 62G05

Additional information

Funding

This work was supported by the Indian National Science Academy (INSA) under the scheme “INSA Senior Scientist” at the CR RAO Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad 500046, India.