Instrumental variable estimation for stochastic differential equations linear in drift parameter and driven by a sub-fractional Brownian motion

ABSTRACT

We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by a sub-fractional Brownian motion.

KEYWORDS:

• Linear stochastic differential equations
• Sub-fractional Brownian motion
• Instrumental variable estimation
• Consistency
• Asymptotic mixed normality

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62M09, Secondary 60G22

Acknowledgement

This work was done under the scheme “Ramanujan Chair Professor” when the author was at the CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad, India.