Höffding-type exponential inequalities are obtained for the distribution tails of canonical von Mises’ statistics of arbitrary order based on samples from a stationary sequence of random variables satisfying the φ-mixing condition.

Let (Xn)n≥1 be a Markov chain on a general state space with stationary distribution π and a spectral gap in the space Lπ2. In this paper, we prove that the probabilities of large deviations of sums Sn=∑k=1nf(Xk) satisfy an inequality of Hoeffding type. We generalize results of León and...