  We study linear eigenvalue statistics of band Hankel matrices with Brownian
motion entries. We prove that, the centred, normalized linear eigenvalue
statistics of band Hankel matrices obey a central limit theorem (CLT) type
result. We also discuss the convergence of linear eigenvalue statistics of band
Hankel matrices with independent entries for odd power monomials. Our method is
based on trace formula, moment method and some results of process convergence.
