On discrete time ergodic filters with wrong initial data, 2

M.L.Kleptsyna & A.Yu.Veretennikov

For a class of non-uniformly ergodic Markov chains satisfying exponential or polynomial beta-mixing, in a Hidden Markov Model under observations subject to an IID noise, it is shown that wrong initial data is forgotten in the mean total variation topology with a certain exponential or polynomial rate. It is allowed that the density of the noise in the signal may vanish. This is a continuation of the part 1 available online, however it can be read completely independently.