Reconstructing a recurrent random environment from a single trajectory of a Random Walk in Random Environment with errors

We consider one infinite path of a Random Walk in Environment (RWRE, for short) an unknown environment. This environment consists either i.i.d. site or bond randomness. At each position the random walker stops and tells us it sees at point where is, without telling us, is. These observations χ′ are spoiled by reading errors that occur with probability p<1. show: If RWRE is recurrent satisfies standard assumptions on such RWREs, then environment, errors, walk we able reconstruct law For most situations this result even independent value p. distribution has non-atomic part, can itself, up to translation.