TY - JOUR A1 - Nielsen, Adam T1 - The Monte Carlo Computation Error of Transition Probabilities T2 - Statistics & Probability Letters N2 - In many applications one is interested to compute transition probabilities of a Markov chain. This can be achieved by using Monte Carlo methods with local or global sampling points. In this article, we analyze the error by the difference in the $L^2$ norm between the true transition probabilities and the approximation achieved through a Monte Carlo method. We give a formula for the error for Markov chains with locally computed sampling points. Further, in the case of reversible Markov chains, we will deduce a formula for the error when sampling points are computed globally. We will see that in both cases the error itself can be approximated with Monte Carlo methods. As a consequence of the result, we will derive surprising properties of reversible Markov chains. Y1 - 2016 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/5994 VL - 118 SP - 163 EP - 170 PB - Elsevier ER -