Donsker-Varadhan's type large deviation will be discussed for the pinned motion of a radial random walk on a homogeneous tree. We shall prove that the rate function corresponding to the large deviation is associated with a new Markov chain constructed from the above random walk through a harmonic transform based on a positive principal eigenfunction for the generator of the random walk.
"Large deviations for radial random walks on homogeneous trees." Nagoya Math. J. 187 75 - 90, 2007.