Large and moderate deviations for the local time of a recurrent Markov chain on Z2

Let (X-n) be a recurrent Markov chain on Z(2) with X-0 = (0,0) such that for some constant C, P[X-k = (0,0)] less than or equal to C/k, and whose truncated Green function is slowly varying at infinity. Let L-n(0) denote the local time at zero of such a Markov chain. We: prove various moderate and large deviation statements and limit laws for rescaled versions of L-n(0), including functional versions of these. A version of Strassen's functional law of the iterated logarithm, recently discovered by E. Csaki, P. Revesz and J. Rosen, can be derived as a corollary. (C) Eisevier, Paris.