Monte Carlo eigenvalue biases: generalization beyond the absorption estimate

In this paper, the author considers the Monte Carlo power method in its simplest form with the fission source normalized after each fission generation and M, the number of neutrons per generation, held constant. It has been shown that in this case, for analog Monte Carlo with an absorption estimator, Δλ=N(σR2) - σAP2/(2λ0), where N=number of generations, λ0=true fundamental-mode eigenvalue, σR2=real variance in the absorption estimate of λ0, σAP2=apparent variance computed as if the per-generation estimates were not correlated. From the equations, on finds that σR/λ0 ≤ 0.25% and N ≤ 800, then Δλ ≤ σR. The author will show that it is true for all methods that can be approximated in discretized phase-space, an approximation assumed in the paper