  We consider the problem of non-parametric density estimation of a random
environment from the observation of a single trajectory of a random walk in
this environment. We first construct a density estimator using the
beta-moments. We then show that the Goldenshluger-Lepski method can be used to
select the beta-moment. We prove non-asymptotic bounds for the supremum norm of
these estimators for both the recurrent and the transient to the right cases. A
simulation study supports our theoretical findings.
