Accelerate Monte Carlo Simulation for Probability Measures by an Interrupt Mechanism

Abstract

Monte Carlo simulation (MCS) is useful for verifying analytical derivations and studying complex systems on an empirical basis. Although MCS is straightforward and does not require a priori knowledge of the sampled probability measures (PMs), it consumes a tremendous amount of computational resource and suffers from slow simulation procedures for sophisticated systems. To mitigate this drawback of MCS, we make full use of the monotone property and the logarithmic presentation convention of PMs in regard to power related metrics (PRMs) in communications science and propose an easy-to-implement interrupt mechanism to accelerate MCS for estimating PMs. To facilitate the programming on different platforms and provide a solid theoretical foundation, we present a generic implementation framework suited for estimating PMs with certain properties by MCS and analyze the underlying theory of the interrupt mechanism. In particular, we apply the de Moivre-Laplace theorem and analytic continuation to prove the asymptotic consistency under the indirect setup of MCS. We also design a hypothesis test for studying the proposed mechanism on a statistical basis.