Eddy Mayer-Wolf

Exact behavior of Gaussian seminorms

The exact lower tail of Gaussian seminorms are evaluated, using a refinement of the techniques presented in Mayer-Wolf and Zeitouni (1993).

On the Memory Length of the Optimal Nonlinear Filter

Consider the standard one-dimensional nonlinear filtering problem with plant diffusion coefficient eγ and observation noise coefficient e1-γ, stationarity of the plant is assumed. Definitions for the memory length of the optimal non-linear filter are suggested and it is shown that the memory length tends to zero as e → 0 for γ 1/2. It is pointed out that while for e → 0, γ 1/2 and an approximate asymptotically optimal non-linear filter is suggested for a particular generic example.