Large and moderate deviations for the local time of a recurrent Markov chain on [formula omitted

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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)] ≤ 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. Csáki, P. Révész and J. Rosen, can be derived as a corollary.