Abstract: Let Wt be a Brownian Motion and in

pendent of Wt. σ, τ> 0 are real, unknown parameters. Suppose we observe Yi,n = σWi/n + τin. In this paper we will establish sharp estimators for σ 2 and τ2 in minimax sense, i.e. they attain asymptotically the minimax constant. A short and direct proof for the minimax lower bound is given. These estimators are based on a spectral decomposition of the underlying process Yi,n and can be com-puted explicitly taking O(n logn) operations. We outline how these estimators can be generalized from Brownian Motion to processes with independent increments. Further we show that the presented spectral estimators are asymptotically normal