Limit theorems for stopped functionals of Markov renewal processes (Q1807969)

Some results of \textit{A. Gut} [``Stopped random walks. Limit theorems and applications'' (1988; Zbl 0634.60061)] are extended to a Markov renewal process for which the usual counting process \((N(t), t\geq 0)\) has inter-arrival times \(X_n\) and associated rewards \(Y_n\) jointly controlled by a Harris-recurrent Markov chain \((M_n, n\geq 0)\). Attention focusses on limit theorems (SLLN, CLT, LIL and moment convergence) for functionals \(\sum^{N(t)}_{n= 1} f(M_n, X_n,Y_n)\). In the proofs extensive use is made of renewal theory for 1-dependent variables according to \textit{S. Janson} [Ann. Probab. 11, 558-568 (1993; Zbl 0514.60086)]. Applications to chromatography are discussed.