An Arcsine Law for Markov Random Walks

Gerold Alsmeyer, Fabian Buckmann

The classic arcsine law for the number $N_n^{>}:=n^{-1}{\sum }_{k=1}^n{1}_{\{S_k>0\}}$ of positive terms, as $n\to \infty$, in an ordinary random walk $(S_n{)}_{n\ge 0}$ i…