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We introduce a simple general method for finding the equilibrium distributionfor a class of widely used inexact Markov Chain Monte Carlo algorithms. Theexplicit error due to the non-commutivity of the updating operators whennumerically integrating Hamilton's equations can be derived using theBaker-Campbell-Hausdorff formula. This error is manifest in the conservation ofa ``shadow'' Hamiltonian that lies close to the desired Hamiltonian. The fixedpoint distribution of inexact Hybrid algorithms may then be derived taking intoaccount that the fixed point of the momentum heatbath and that of the moleculardynamics do not coincide exactly. We perform this derivation for variousinexact algorithms used for lattice QCD calculations.

Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms