Optimal estimation of a signal perturbed by a sub-fractional Brownian motion

ABSTRACT

We consider the problem of optimal estimation of the vector parameter θ of the drift term in a sub-fractional Brownian motion. We obtain the maximum likelihood estimator as well as Bayesian estimator when the prior distribution is Gaussian.

KEYWORDS:

• Sub-fractional Brownian motion
• maximum likelihood estimation
• Bayes estimation

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G22

Funding

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